You can do functional programming in Lisp, but even the wiki page for GOAL says "GOAL encourages an imperative programming style". Not to mention most Lisp data structures being mutable if we're talking purely functional.
I looks like alayne is using 'purely functional' to mean Pure + Functional, but you are using it to mean Everything is an Expression / First-class functions, etc.. The functional paradigm.
Lisp is definitely a functional language. It's just not as pure as Haskell, which is the poster child for Maximally Pure FP, if not for the functional style.