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Lisp is not a FP. It's a "List processing language" with some features based on Lambda calculus.

Real FP means referential transparency and that started with languages like Miranda and later Haskell.

What many people consider "FP" today is in fact just procedural programming with higher order procedures and lexical closure.

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Lisp is even not a language, it's a family of languages. It started as a "LISt Processor", but it

A lot of early FP teaching was done in Lisp. Some kind of "Pure Lisp" was used, which are imaginary subsets of Lisp, restricted to side-effect-free, non-destructive functions.

FP started quite a bit before Miranda.

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