For some definition of "functional" that was appropriate when LISP was discovered, and of course any claim about LISP tends to be met with, "which one?"
LISP really deserves to be "grandfathered in" as the original functional programming language, but if it were discovered today, we'd likely call it a multi-paradigm language that supports functions as first-class entities.
And as a "programmable programming language," we can use LISP to implement many other paradigms, including what we now consider "functional" programming.
Lisp's development was skewed by the high cost of memory. Early on, scope was dynamic, lists were mutable and often spliced in-place, linear searches were typical (hash tables were almost unheard of), and there were very few first-class types because a pointer only had so many tag bits available.
Things evolved in the 70s. Hash tables were added over time, with some alternatives were using some tree like search. Usually the first thing was to make the symbol table not a list -> making the symbol table a hash table was reportedly done in 1971 by Jon L White. Tag bits then also were not a part of the pointers (with only very few exceptions), but a part of the data object (numbers, strings, arrays, symbols, ..).