diff --git a/spring-integration-core/src/main/java/org/springframework/integration/handler/LambdaMessageProcessor.java b/spring-integration-core/src/main/java/org/springframework/integration/handler/LambdaMessageProcessor.java
index 8fa40651fb1..ff74f83dba4 100644
--- a/spring-integration-core/src/main/java/org/springframework/integration/handler/LambdaMessageProcessor.java
+++ b/spring-integration-core/src/main/java/org/springframework/integration/handler/LambdaMessageProcessor.java
@@ -1,5 +1,5 @@
 /*
- * Copyright 2016-2021 the original author or authors.
+ * Copyright 2016-2022 the original author or authors.
  *
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
@@ -21,6 +21,7 @@
 import java.lang.reflect.Modifier;
 import java.util.Map;
 import java.util.Set;
+import java.util.function.Function;
 
 import org.apache.commons.logging.Log;
 import org.apache.commons.logging.LogFactory;
@@ -31,8 +32,11 @@
 import org.springframework.core.MethodIntrospector;
 import org.springframework.core.log.LogMessage;
 import org.springframework.integration.context.IntegrationContextUtils;
+import org.springframework.integration.core.GenericSelector;
+import org.springframework.integration.transformer.GenericTransformer;
 import org.springframework.lang.Nullable;
 import org.springframework.messaging.Message;
+import org.springframework.messaging.MessageHeaders;
 import org.springframework.messaging.converter.MessageConverter;
 import org.springframework.util.Assert;
 import org.springframework.util.ClassUtils;
@@ -85,11 +89,20 @@ public LambdaMessageProcessor(Object target, @Nullable Class<?> expectedType) {
 						"classes with single method - functional interface implementations.");
 
 		this.method = methods.iterator().next();
-		ReflectionUtils.makeAccessible(this.method);
+		if (!isExplicit(target)) {
+			ReflectionUtils.makeAccessible(this.method);
+		}
 		this.parameterTypes = this.method.getParameterTypes();
 		this.expectedType = expectedType;
 	}
 
+	private static boolean isExplicit(Object target) {
+		return target instanceof Function<?, ?> ||
+				target instanceof GenericHandler<?> ||
+				target instanceof GenericSelector<?> ||
+				target instanceof GenericTransformer<?, ?>;
+	}
+
 	@Override
 	public void setBeanFactory(BeanFactory beanFactory) throws BeansException {
 		this.messageConverter =
@@ -102,20 +115,22 @@ public Object processMessage(Message<?> message) {
 		Object[] args = buildArgs(message);
 
 		try {
-			Object result = this.method.invoke(this.target, args);
+			Object result = invokeMethod(args);
 			if (result != null && org.springframework.integration.util.ClassUtils.isKotlinUnit(result.getClass())) {
 				result = null;
 			}
 			return result;
 		}
+		catch (RuntimeException ex) {
+			if (ex instanceof ClassCastException classCastException) {
+				logClassCastException(classCastException);
+			}
+			throw ex;
+		}
 		catch (InvocationTargetException e) {
 			final Throwable cause = e.getCause();
-			if (e.getTargetException() instanceof ClassCastException) {
-				LOGGER.error("Could not invoke the method '" + this.method + "' due to a class cast exception, " +
-						"if using a lambda in the DSL, consider using an overloaded EIP method " +
-						"that takes a Class<?> argument to explicitly  specify the type. " +
-						"An example of when this often occurs is if the lambda is configured to " +
-						"receive a Message<?> argument.", cause);
+			if (e.getTargetException() instanceof ClassCastException classCastException) {
+				logClassCastException(classCastException);
 			}
 			if (cause instanceof RuntimeException) { // NOSONAR
 				throw (RuntimeException) cause;
@@ -170,4 +185,41 @@ else if (Map.class.isAssignableFrom(parameterType)) {
 		return args;
 	}
 
+	@SuppressWarnings({ "unchecked", "rawtypes" })
+	private Object invokeMethod(Object[] args) throws InvocationTargetException, IllegalAccessException {
+		if (this.target instanceof Function function) {
+			return function.apply(args[0]);
+		}
+		else if (this.target instanceof GenericSelector selector) {
+			return selector.accept(args[0]);
+		}
+		else if (this.target instanceof GenericTransformer transformer) {
+			return transformer.transform(args[0]);
+		}
+		else if (this.target instanceof GenericHandler handler) {
+			return handler.handle(args[0], (MessageHeaders) args[1]);
+		}
+		else {
+			return this.method.invoke(this.target, args);
+		}
+
+		/* TODO when preview features are available in the next Java version
+		return switch (this.target) {
+			case Function function -> function.apply(args[0]);
+			case GenericSelector selector -> selector.accept(args[0]);
+			case GenericTransformer transformer -> transformer.transform(args[0]);
+			case GenericHandler handler -> handler.handle(args[0], (MessageHeaders) args[1]);
+			default -> this.method.invoke(this.target, args);
+		};
+*/
+	}
+
+	private void logClassCastException(ClassCastException classCastException) {
+		LOGGER.error("Could not invoke the method '" + this.method + "' due to a class cast exception, " +
+				"if using a lambda in the DSL, consider using an overloaded EIP method " +
+				"that takes a Class<?> argument to explicitly  specify the type. " +
+				"An example of when this often occurs is if the lambda is configured to " +
+				"receive a Message<?> argument.", classCastException);
+	}
+
 }
diff --git a/spring-integration-core/src/test/java/org/springframework/integration/dsl/LambdaMessageProcessorTests.java b/spring-integration-core/src/test/java/org/springframework/integration/dsl/LambdaMessageProcessorTests.java
index 5fb2a6e4606..55d4783255b 100644
--- a/spring-integration-core/src/test/java/org/springframework/integration/dsl/LambdaMessageProcessorTests.java
+++ b/spring-integration-core/src/test/java/org/springframework/integration/dsl/LambdaMessageProcessorTests.java
@@ -23,7 +23,6 @@
 import java.util.Objects;
 import java.util.function.Function;
 
-import org.junit.jupiter.api.Disabled;
 import org.junit.jupiter.api.Test;
 
 import org.springframework.beans.factory.BeanFactory;
@@ -107,7 +106,6 @@ public boolean accept(Date payload) {
 
 
 	@Test
-	@Disabled("Until https://github.com/spring-projects/spring-integration/issues/3660")
 	public void testCustomConverter() {
 		LambdaMessageProcessor lmp = new LambdaMessageProcessor(Function.identity(), TestPojo.class);
 		lmp.setBeanFactory(this.beanFactory);