> Immutable objects do not have identity and are values.

Really? https://ideone.com/mmQJGr

> And the distinction between primitives and objects in Java, for our discussion here, is irrelevant.

All it takes to disabuse you of this notion is a little bit of reflection.

> That Haskell can force purity via its laziness

This is not true. Purity is enforced via the type system.

> but not required for doing FP, just like how static types aren't required for doing FP either

Completely agree here.

> but they've been preceded by LISP and ML.

ML is a functional language. Scheme already forces you to squint your eyes a lot. Lisp is not a functional language by any stretch of the term's meaning.