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.
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.