People are now trying to redefine what functional programming means. Lisp is as close to the lambda calculus as you can get, and Functional Programming is based on lambda calculus mode of computation (VS Von Neumann procedural model).

When you write Lisp, you're mostly composing functions. It's truly very functional, just not purely functional which is probably the motivation behind your refusal to include Lisp in the functional programming language family, which would horrify the founders of the field as it's a simple attempt at redefining a widely used, well understood term to become a small subset of it for reasons of gatekeeping what we should, according to you, include under the term without any real technical reason behind it.