Java 8 lambda Void argument

Use Supplier if it takes nothing, but returns something.

Use Consumer if it takes something, but returns nothing.

Use Callable if it returns a result and might throw (most akin to Thunk in general CS terms).

Use Runnable if it does neither and cannot throw.

The syntax you're after is possible with a little helper function that converts a Runnable into Action<Void, Void> (you can place it in Action for example):

public static Action<Void, Void> action(Runnable runnable) {
    return (v) -> {
        runnable.run();
        return null;
    };
}

// Somewhere else in your code
 Action<Void, Void> action = action(() -> System.out.println("foo"));

I think this table is short and usefull:

Supplier       ()    -> x
Consumer       x     -> ()
BiConsumer     x, y  -> ()
Callable       ()    -> x throws ex
Runnable       ()    -> ()
Function       x     -> y
BiFunction     x,y   -> z
Predicate      x     -> boolean
UnaryOperator  x1    -> x2
BinaryOperator x1,x2 -> x3

As said on the other answers, the appropriate option for this problem is a Runnable

The lambda:

() -> { System.out.println("Do nothing!"); };

actually represents an implementation for an interface like:

public interface Something {
    void action();
}

which is completely different than the one you've defined. That's why you get an error.

Since you can't extend your @FunctionalInterface, nor introduce a brand new one, then I think you don't have much options. You can use the Optional<T> interfaces to denote that some of the values (return type or method parameter) is missing, though. However, this won't make the lambda body simpler.