This works fine:

@Configuration
public class MappingConverterConfig {

    @Bean
    public Converter<String, LocalDate> stringLocalDateConverter() {
        return new Converter<String, LocalDate>() {
            @Override
            public LocalDate convert(String source) {
                return LocalDate.parse(source);
            }
        };
    }

}

This does not work:

@Bean
    public Converter<String, LocalDate> stringLocalDateConverter() {
        return LocalDate::parse;
    }

Log:

"C:\Program Files\Java\jdk-11.0.2\bin\java.exe" -agentlib:jdwp=transport=dt_socket,address=127.0.0.1:54901,suspend=y,server=n -XX:TieredStopAtLevel=1 -noverify -Dspring.output.ansi.enabled=always -Dcom.sun.management.jmxremote -Dspring.liveBeansView.mbeanDomain -Dspring.application.admin.enabled=true -javaagent:C:\Users\Sofior\.IntelliJIdea2018.3\system\captureAgent\debugger-agent.jar -Dfile.encoding=UTF-8 -classpath "C:\Users\Sofior\#code\private\house\target\classes;C:\Users\Sofior\.m2\repository\org\springframework\boot\spring-boot-starter-aop\2.1.3.RELEASE\spring-boot-starter-aop-2.1.3.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\springframework\boot\spring-boot-starter\2.1.3.RELEASE\spring-boot-starter-2.1.3.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\springframework\boot\spring-boot-starter-logging\2.1.3.RELEASE\spring-boot-starter-logging-2.1.3.RELEASE.jar;C:\Users\Sofior\.m2\repository\ch\qos\logback\logback-classic\1.2.3\logback-classic-1.2.3.jar;C:\Users\Sofior\.m2\repository\ch\qos\logback\logback-core\1.2.3\logback-core-1.2.3.jar;C:\Users\Sofior\.m2\repository\org\apache\logging\log4j\log4j-to-slf4j\2.11.2\log4j-to-slf4j-2.11.2.jar;C:\Users\Sofior\.m2\repository\org\apache\logging\log4j\log4j-api\2.11.2\log4j-api-2.11.2.jar;C:\Users\Sofior\.m2\repository\org\slf4j\jul-to-slf4j\1.7.25\jul-to-slf4j-1.7.25.jar;C:\Users\Sofior\.m2\repository\javax\annotation\javax.annotation-api\1.3.2\javax.annotation-api-1.3.2.jar;C:\Users\Sofior\.m2\repository\org\yaml\snakeyaml\1.23\snakeyaml-1.23.jar;C:\Users\Sofior\.m2\repository\org\springframework\spring-aop\5.1.5.RELEASE\spring-aop-5.1.5.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\springframework\spring-beans\5.1.5.RELEASE\spring-beans-5.1.5.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\aspectj\aspectjweaver\1.9.2\aspectjweaver-1.9.2.jar;C:\Users\Sofior\.m2\repository\org\springframework\boot\spring-boot-starter-validation\2.1.3.RELEASE\spring-boot-starter-validation-2.1.3.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\apache\tomcat\embed\tomcat-embed-el\9.0.16\tomcat-embed-el-9.0.16.jar;C:\Users\Sofior\.m2\repository\org\hibernate\validator\hibernate-validator\6.0.14.Final\hibernate-validator-6.0.14.Final.jar;C:\Users\Sofior\.m2\repository\javax\validation\validation-api\2.0.1.Final\validation-api-2.0.1.Final.jar;C:\Users\Sofior\.m2\repository\org\jboss\logging\jboss-logging\3.3.2.Final\jboss-logging-3.3.2.Final.jar;C:\Users\Sofior\.m2\repository\com\fasterxml\classmate\1.4.0\classmate-1.4.0.jar;C:\Users\Sofior\.m2\repository\org\springframework\boot\spring-boot-starter-webflux\2.1.3.RELEASE\spring-boot-starter-webflux-2.1.3.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\springframework\boot\spring-boot-starter-json\2.1.3.RELEASE\spring-boot-starter-json-2.1.3.RELEASE.jar;C:\Users\Sofior\.m2\repository\com\fasterxml\jackson\core\jackson-databind\2.9.8\jackson-databind-2.9.8.jar;C:\Users\Sofior\.m2\repository\com\fasterxml\jackson\core\jackson-annotations\2.9.0\jackson-annotations-2.9.0.jar;C:\Users\Sofior\.m2\repository\com\fasterxml\jackson\core\jackson-core\2.9.8\jackson-core-2.9.8.jar;C:\Users\Sofior\.m2\repository\com\fasterxml\jackson\datatype\jackson-datatype-jdk8\2.9.8\jackson-datatype-jdk8-2.9.8.jar;C:\Users\Sofior\.m2\repository\com\fasterxml\jackson\datatype\jackson-datatype-jsr310\2.9.8\jackson-datatype-jsr310-2.9.8.jar;C:\Users\Sofior\.m2\repository\com\fasterxml\jackson\module\jackson-module-parameter-names\2.9.8\jackson-module-parameter-names-2.9.8.jar;C:\Users\Sofior\.m2\repository\org\springframework\boot\spring-boot-starter-reactor-netty\2.1.3.RELEASE\spring-boot-starter-reactor-netty-2.1.3.RELEASE.jar;C:\Users\Sofior\.m2\repository\io\projectreactor\netty\reactor-netty\0.8.5.RELEASE\reactor-netty-0.8.5.RELEASE.jar;C:\Users\Sofior\.m2\repository\io\netty\netty-codec-http\4.1.33.Final\netty-codec-http-4.1.33.Final.jar;C:\Users\Sofior\.m2\repository\io\netty\netty-common\4.1.33.Final\netty-common-4.1.33.Final.jar;C:\Users\Sofior\.m2\repository\io\netty\netty-buffer\4.1.33.Final\netty-buffer-4.1.33.Final.jar;C:\Users\Sofior\.m2\repository\io\netty\netty-transport\4.1.33.Final\netty-transport-4.1.33.Final.jar;C:\Users\Sofior\.m2\repository\io\netty\netty-resolver\4.1.33.Final\netty-resolver-4.1.33.Final.jar;C:\Users\Sofior\.m2\repository\io\netty\netty-codec\4.1.33.Final\netty-codec-4.1.33.Final.jar;C:\Users\Sofior\.m2\repository\io\netty\netty-codec-http2\4.1.33.Final\netty-codec-http2-4.1.33.Final.jar;C:\Users\Sofior\.m2\repository\io\netty\netty-handler\4.1.33.Final\netty-handler-4.1.33.Final.jar;C:\Users\Sofior\.m2\repository\io\netty\netty-handler-proxy\4.1.33.Final\netty-handler-proxy-4.1.33.Final.jar;C:\Users\Sofior\.m2\repository\io\netty\netty-codec-socks\4.1.33.Final\netty-codec-socks-4.1.33.Final.jar;C:\Users\Sofior\.m2\repository\io\netty\netty-transport-native-epoll\4.1.33.Final\netty-transport-native-epoll-4.1.33.Final-linux-x86_64.jar;C:\Users\Sofior\.m2\repository\io\netty\netty-transport-native-unix-common\4.1.33.Final\netty-transport-native-unix-common-4.1.33.Final.jar;C:\Users\Sofior\.m2\repository\org\springframework\spring-web\5.1.5.RELEASE\spring-web-5.1.5.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\springframework\spring-webflux\5.1.5.RELEASE\spring-webflux-5.1.5.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\synchronoss\cloud\nio-multipart-parser\1.1.0\nio-multipart-parser-1.1.0.jar;C:\Users\Sofior\.m2\repository\org\slf4j\slf4j-api\1.7.25\slf4j-api-1.7.25.jar;C:\Users\Sofior\.m2\repository\org\synchronoss\cloud\nio-stream-storage\1.1.3\nio-stream-storage-1.1.3.jar;C:\Users\Sofior\.m2\repository\org\springframework\boot\spring-boot-devtools\2.1.3.RELEASE\spring-boot-devtools-2.1.3.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\springframework\boot\spring-boot\2.1.3.RELEASE\spring-boot-2.1.3.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\springframework\spring-context\5.1.5.RELEASE\spring-context-5.1.5.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\springframework\spring-expression\5.1.5.RELEASE\spring-expression-5.1.5.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\springframework\boot\spring-boot-autoconfigure\2.1.3.RELEASE\spring-boot-autoconfigure-2.1.3.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\springframework\boot\spring-boot-configuration-processor\2.1.3.RELEASE\spring-boot-configuration-processor-2.1.3.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\projectlombok\lombok\1.18.6\lombok-1.18.6.jar;C:\Users\Sofior\.m2\repository\org\springframework\spring-core\5.1.5.RELEASE\spring-core-5.1.5.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\springframework\spring-jcl\5.1.5.RELEASE\spring-jcl-5.1.5.RELEASE.jar;C:\Users\Sofior\.m2\repository\io\projectreactor\reactor-core\3.2.6.RELEASE\reactor-core-3.2.6.RELEASE.jar;C:\Users\Sofior\.m2\repository\org\reactivestreams\reactive-streams\1.0.2\reactive-streams-1.0.2.jar;C:\Program Files\JetBrains\IntelliJ IDEA 2018.3\lib\idea_rt.jar" site.ownw.micro.house.HouseApplication
Connected to the target VM, address: '127.0.0.1:54901', transport: 'socket'

  .   ____          _            __ _ _
 /\\ / ___'_ __ _ _(_)_ __  __ _ \ \ \ \
( ( )\___ | '_ | '_| | '_ \/ _` | \ \ \ \
 \\/  ___)| |_)| | | | | || (_| |  ) ) ) )
  '  |____| .__|_| |_|_| |_\__, | / / / /
 =========|_|==============|___/=/_/_/_/
 :: Spring Boot ::        (v2.1.3.RELEASE)

2019-03-05 14:59:16.454  INFO 18492 --- [  restartedMain] site.ownw.micro.house.HouseApplication   : Starting HouseApplication on Sofior-XYD with PID 18492 (started by Sofior in C:\Users\Sofior\#code\private\house)
2019-03-05 14:59:16.456  INFO 18492 --- [  restartedMain] site.ownw.micro.house.HouseApplication   : No active profile set, falling back to default profiles: default
2019-03-05 14:59:16.491  INFO 18492 --- [  restartedMain] .e.DevToolsPropertyDefaultsPostProcessor : Devtools property defaults active! Set 'spring.devtools.add-properties' to 'false' to disable
2019-03-05 14:59:16.492  INFO 18492 --- [  restartedMain] .e.DevToolsPropertyDefaultsPostProcessor : For additional web related logging consider setting the 'logging.level.web' property to 'DEBUG'
2019-03-05 14:59:20.500  WARN 18492 --- [  restartedMain] onfigReactiveWebServerApplicationContext : Exception encountered during context initialization - cancelling refresh attempt: org.springframework.beans.factory.BeanCreationException: Error creating bean with name 'webFluxConversionService' defined in class path resource [org/springframework/boot/autoconfigure/web/reactive/WebFluxAutoConfiguration$EnableWebFluxConfiguration.class]: Bean instantiation via factory method failed; nested exception is org.springframework.beans.BeanInstantiationException: Failed to instantiate [org.springframework.format.support.FormattingConversionService]: Factory method 'webFluxConversionService' threw exception; nested exception is java.lang.IllegalArgumentException: Unable to determine source type <S> and target type <T> for your Converter [site.ownw.micro.house.config.MappingConverterConfig$$Lambda$380/0x00000008003e4840]; does the class parameterize those types?
2019-03-05 14:59:20.523  INFO 18492 --- [  restartedMain] ConditionEvaluationReportLoggingListener : 

Error starting ApplicationContext. To display the conditions report re-run your application with 'debug' enabled.
2019-03-05 14:59:20.534 ERROR 18492 --- [  restartedMain] o.s.boot.SpringApplication               : Application run failed

org.springframework.beans.factory.BeanCreationException: Error creating bean with name 'webFluxConversionService' defined in class path resource [org/springframework/boot/autoconfigure/web/reactive/WebFluxAutoConfiguration$EnableWebFluxConfiguration.class]: Bean instantiation via factory method failed; nested exception is org.springframework.beans.BeanInstantiationException: Failed to instantiate [org.springframework.format.support.FormattingConversionService]: Factory method 'webFluxConversionService' threw exception; nested exception is java.lang.IllegalArgumentException: Unable to determine source type <S> and target type <T> for your Converter [site.ownw.micro.house.config.MappingConverterConfig$$Lambda$380/0x00000008003e4840]; does the class parameterize those types?
    at org.springframework.beans.factory.support.ConstructorResolver.instantiate(ConstructorResolver.java:627) ~[spring-beans-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.beans.factory.support.ConstructorResolver.instantiateUsingFactoryMethod(ConstructorResolver.java:607) ~[spring-beans-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.instantiateUsingFactoryMethod(AbstractAutowireCapableBeanFactory.java:1305) ~[spring-beans-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.createBeanInstance(AbstractAutowireCapableBeanFactory.java:1144) ~[spring-beans-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.doCreateBean(AbstractAutowireCapableBeanFactory.java:555) ~[spring-beans-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.createBean(AbstractAutowireCapableBeanFactory.java:515) ~[spring-beans-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.beans.factory.support.AbstractBeanFactory.lambda$doGetBean$0(AbstractBeanFactory.java:320) ~[spring-beans-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.beans.factory.support.DefaultSingletonBeanRegistry.getSingleton(DefaultSingletonBeanRegistry.java:222) ~[spring-beans-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.beans.factory.support.AbstractBeanFactory.doGetBean(AbstractBeanFactory.java:318) ~[spring-beans-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.beans.factory.support.AbstractBeanFactory.getBean(AbstractBeanFactory.java:199) ~[spring-beans-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.beans.factory.support.DefaultListableBeanFactory.preInstantiateSingletons(DefaultListableBeanFactory.java:849) ~[spring-beans-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.context.support.AbstractApplicationContext.finishBeanFactoryInitialization(AbstractApplicationContext.java:877) ~[spring-context-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.context.support.AbstractApplicationContext.refresh(AbstractApplicationContext.java:549) ~[spring-context-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.boot.web.reactive.context.ReactiveWebServerApplicationContext.refresh(ReactiveWebServerApplicationContext.java:67) ~[spring-boot-2.1.3.RELEASE.jar:2.1.3.RELEASE]
    at org.springframework.boot.SpringApplication.refresh(SpringApplication.java:775) ~[spring-boot-2.1.3.RELEASE.jar:2.1.3.RELEASE]
    at org.springframework.boot.SpringApplication.refreshContext(SpringApplication.java:397) ~[spring-boot-2.1.3.RELEASE.jar:2.1.3.RELEASE]
    at org.springframework.boot.SpringApplication.run(SpringApplication.java:316) ~[spring-boot-2.1.3.RELEASE.jar:2.1.3.RELEASE]
    at org.springframework.boot.SpringApplication.run(SpringApplication.java:1260) ~[spring-boot-2.1.3.RELEASE.jar:2.1.3.RELEASE]
    at org.springframework.boot.SpringApplication.run(SpringApplication.java:1248) ~[spring-boot-2.1.3.RELEASE.jar:2.1.3.RELEASE]
    at site.ownw.micro.house.HouseApplication.main(HouseApplication.java:10) ~[classes/:na]
    at java.base/jdk.internal.reflect.NativeMethodAccessorImpl.invoke0(Native Method) ~[na:na]
    at java.base/jdk.internal.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62) ~[na:na]
    at java.base/jdk.internal.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43) ~[na:na]
    at java.base/java.lang.reflect.Method.invoke(Method.java:566) ~[na:na]
    at org.springframework.boot.devtools.restart.RestartLauncher.run(RestartLauncher.java:49) ~[spring-boot-devtools-2.1.3.RELEASE.jar:2.1.3.RELEASE]
Caused by: org.springframework.beans.BeanInstantiationException: Failed to instantiate [org.springframework.format.support.FormattingConversionService]: Factory method 'webFluxConversionService' threw exception; nested exception is java.lang.IllegalArgumentException: Unable to determine source type <S> and target type <T> for your Converter [site.ownw.micro.house.config.MappingConverterConfig$$Lambda$380/0x00000008003e4840]; does the class parameterize those types?
    at org.springframework.beans.factory.support.SimpleInstantiationStrategy.instantiate(SimpleInstantiationStrategy.java:185) ~[spring-beans-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.beans.factory.support.ConstructorResolver.instantiate(ConstructorResolver.java:622) ~[spring-beans-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    ... 24 common frames omitted
Caused by: java.lang.IllegalArgumentException: Unable to determine source type <S> and target type <T> for your Converter [site.ownw.micro.house.config.MappingConverterConfig$$Lambda$380/0x00000008003e4840]; does the class parameterize those types?
    at org.springframework.core.convert.support.GenericConversionService.addConverter(GenericConversionService.java:92) ~[spring-core-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.boot.autoconfigure.web.reactive.WebFluxAutoConfiguration$WebFluxConfig.addFormatters(WebFluxAutoConfiguration.java:186) ~[spring-boot-autoconfigure-2.1.3.RELEASE.jar:2.1.3.RELEASE]
    at org.springframework.web.reactive.config.WebFluxConfigurerComposite.lambda$addFormatters$6(WebFluxConfigurerComposite.java:85) ~[spring-webflux-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at java.base/java.util.ArrayList.forEach(ArrayList.java:1540) ~[na:na]
    at org.springframework.web.reactive.config.WebFluxConfigurerComposite.addFormatters(WebFluxConfigurerComposite.java:85) ~[spring-webflux-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.web.reactive.config.DelegatingWebFluxConfiguration.addFormatters(DelegatingWebFluxConfiguration.java:84) ~[spring-webflux-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.boot.autoconfigure.web.reactive.WebFluxAutoConfiguration$EnableWebFluxConfiguration.webFluxConversionService(WebFluxAutoConfiguration.java:232) ~[spring-boot-autoconfigure-2.1.3.RELEASE.jar:2.1.3.RELEASE]
    at org.springframework.boot.autoconfigure.web.reactive.WebFluxAutoConfiguration$EnableWebFluxConfiguration$$EnhancerBySpringCGLIB$$17b2456c.CGLIB$webFluxConversionService$3(<generated>) ~[spring-boot-autoconfigure-2.1.3.RELEASE.jar:2.1.3.RELEASE]
    at org.springframework.boot.autoconfigure.web.reactive.WebFluxAutoConfiguration$EnableWebFluxConfiguration$$EnhancerBySpringCGLIB$$17b2456c$$FastClassBySpringCGLIB$$cf090196.invoke(<generated>) ~[spring-boot-autoconfigure-2.1.3.RELEASE.jar:2.1.3.RELEASE]
    at org.springframework.cglib.proxy.MethodProxy.invokeSuper(MethodProxy.java:244) ~[spring-core-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.context.annotation.ConfigurationClassEnhancer$BeanMethodInterceptor.intercept(ConfigurationClassEnhancer.java:363) ~[spring-context-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    at org.springframework.boot.autoconfigure.web.reactive.WebFluxAutoConfiguration$EnableWebFluxConfiguration$$EnhancerBySpringCGLIB$$17b2456c.webFluxConversionService(<generated>) ~[spring-boot-autoconfigure-2.1.3.RELEASE.jar:2.1.3.RELEASE]
    at java.base/jdk.internal.reflect.NativeMethodAccessorImpl.invoke0(Native Method) ~[na:na]
    at java.base/jdk.internal.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62) ~[na:na]
    at java.base/jdk.internal.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43) ~[na:na]
    at java.base/java.lang.reflect.Method.invoke(Method.java:566) ~[na:na]
    at org.springframework.beans.factory.support.SimpleInstantiationStrategy.instantiate(SimpleInstantiationStrategy.java:154) ~[spring-beans-5.1.5.RELEASE.jar:5.1.5.RELEASE]
    ... 25 common frames omitted

Disconnected from the target VM, address: '127.0.0.1:54901', transport: 'socket'

Process finished with exit code 0

Comment From: jhoeller

Unfortunately, due to general Java limitations, such lambda expression instances do not retain generic type information, whereas an inner class does contain generic type information in its implementation signature. Since you're relying on Spring Boot's auto-configuration, providing plain converter beans, the conversion service needs to find that generic type information in the converter instances. Alternatively, you could inject the GenericConversionService and register the converter programmatically, specifying the source and target type explicitly: addConverter(String.class, LocalDate.class, LocalDate::parse)