You are also not getting the point you complain about completely clear, it is not that "Lisp isn't really that functional", Lisp != Common Lisp and being a Lisp

You are also not getting the point you complain about completely clear, it is not that "Lisp isn't really that functional", Lisp != Common Lisp and being a Lisp and being functional is to some extent orthogonal those days - Clojure is a very functional Lisp for example, similarly Racket, Common Lisp much less so. The original McCarthy Lisp paper was to a large extent a paper in theory of computation, using Lisp as a vehicle for things like proving program correctness, so that Lisp was purely functional, otherwise you could not do much formal reasoning with it. I guess to be completely clear one has first to define what one means by "Lisp".