This is just not true. The Lisp family contains all conceivable variants of languages, from statically typed Coalton, to dynamically typed Scheme. From functional, immutable by default Clojure to the imperative-style of Common Lisp.
There are prologs, constraint solvers, ffis, JavaScript alternatives, garbage collected and not garbage collected languages that call themselves lisps.
I won't disagree but most books and people who made lisp in the early decades were somehow hinting at not manipulating state but trying to represent ideas and operators to raise the level of expressiveness without shooting yourself in the foot (as much as possible)