@FunctionalInterface annotation is useful for compilation time checking of your code. You cannot have more than one method besides static, default and abstract methods that override methods in Object in your @FunctionalInterface or any other interface used as a functional interface.

But you can use lambdas without this annotation as well as you can override methods without @Override annotation.

From docs

a functional interface has exactly one abstract method. Since default methods have an implementation, they are not abstract. If an interface declares an abstract method overriding one of the public methods of java.lang.Object, that also does not count toward the interface's abstract method count since any implementation of the interface will have an implementation from java.lang.Object or elsewhere

This can be used in lambda expression:

public interface Foo {
  public void doSomething();
}

This cannot be used in lambda expression:

public interface Foo {
  public void doSomething();
  public void doSomethingElse();
}

But this will give compilation error:

@FunctionalInterface
public interface Foo {
  public void doSomething();
  public void doSomethingElse();
}

Invalid '@FunctionalInterface' annotation; Foo is not a functional interface

Your questions could be answered if you read manual about functional interfaces and lambdas. Just take a look on difference between lambda expression and usual anonymous class creation. Both variables can be used the same way.

    //using anonymous class 
    Predicate<String> isStringEmptyObj = new Predicate<String>() {
        @Override
        public boolean test(String o) {
            return o.isEmpty();
        }
    };
    System.out.println(isStringEmptyObj.negate().test("asd"));

    //using lambda with reference to existing String object method
    Predicate<String> isStringEmpty = String::isEmpty;
    System.out.println(isStringEmpty.negate().test("asd"));