Are there other “constant” lambdas like Function.identity()?

No, but for many such “constant” functions it’s easy to write your own lambda expression. In fact, one can write x -> x instead of Function.identity() and in some cases it’s clearer. Here is a list of common constant functions and how they can be written using lambda.

Predicate that always returns true or false:

x -> true
x -> false

Runnable that does nothing:

() -> { }

Consumer that does nothing:

x -> { }

Supplier that returns a constant k. This could be a value that’s captured from the lexical environment, or it could be a literal:

() -> k

Function that returns a constant k:

x -> k

Identity function, the same as Function.identity():

x -> x

Function taking two arguments that returns the first or second:

(a, b) -> a
(a, b) -> b