My Symbolics Lisp Machine has a Lisp implementation where some form of vectors are an optimization of lists (-> CDR coding). But that's an implementation detail. For most purposes the thing behaves as it uses linked lists - and even has primitive operators for linked lists as CPU instructions.
CLISP, another Lisp implementation, has its own virtual machine, written in C. There too, CAR, CDR, CONS are primitive operations in the VM:
[1]> (defun foo (list) (cons (cdr list) (car list)))
FOO
[2]> (disassemble #'foo)
Disassembly of function FOO
1 required argument
0 optional arguments
No rest parameter
No keyword parameters
5 byte-code instructions:
0 (LOAD&CDR&PUSH 1)
2 (LOAD 2)
3 (CAR)
4 (CONS)
5 (SKIP&RET 2)
Then there is this meaning that Lisp is a very diverse group of languages bases on largely undefined criteria. Like C is a member of the ALGOL language family.
That's the "Lisp family": It includes JavaScript/ECMAScript, Dylan, Clojure, Scheme, Racket, R, SKILL... Some have s-expressions, some not. Some use linked lists, some not. Some are object-oriented, some not. And so on.
But for practical purposes it's meaningless: if I want to know about how a particular Scheme construct works, I would look into a Scheme documentation (or its particular implementation), not into a Lisp book.
Scheme, Clojure, .. all have their own language family by now: there are language definitions, a bunch of similar implementations, shared code, books, ...
It's also funny how people claim that language X is a Lisp, as if that would mean something "special" or even "better". There are lots of excellent and useful programming languages out there, which are not Lisp.