Is there a method reference for a no-op (NOP) that can be used for anything lambda?

This is no deficiency.

Lambdas in Java are instances of functional interfaces; which, in turn, are abstracted to instances of Java constructs which can be simplified to one single abstract method, or SAM.

But this SAM still needs to have a valid prototype. In your case, you want to have a no-op Consumer<T> which does nothing whatever the T.

It still needs to be a Consumer<T> however; which means the minimal declaration you can come up with is:

private static final Consumer<Object> NOOP = whatever -> {};

and use NOOP where you need to.

In your particular case you could simply do:

foo(i -> {});

This means that the lambda expression receives a parameter but has no return value.

The equivalent code for a BiConsumer<T, U> would be:

void bifoo(BiConsumer<Object, Object> consumer) { ... }

bifoo((a, b) -> {});

Could Function.identity() fit your needs?

Returns a function that always returns its input argument.