In Common Lisp and its antecedents, a "list" is a chain of cons cells, as mentioned by some of the sibling comments, but that's not all. Another important point is that in Common Lisp and its antecedents, source code is not made of text strings; it's made of Lisp data structures--atoms and chains of cons cells.
A text file containing "Common Lisp source code" does not actually contain Common Lisp source code. It contains a text serialization of Common Lisp source code (one of many possible text serializations, actually). It isn't actually Common Lisp source code until the reader gets done with it.
This might sound like a trivial pedantic point, but it isn't. Because Common Lisp source code is made up of standard Common Lisp data types, its standard library provides everything you need to walk arbitrary source code, deconstruct it, transform it, construct it, and compile it. Those features are all built into the language in a way that they are not in most languages.
For those of us who are accustomed to using those features regularly, working with a language that lacks them is such an impoverished experience that I can understand folks objecting that "that's not a proper Lisp." I don't tend to make that objection myself, but I do understand it.
If your Lisp does not represent its source code in this way, or if it doesn't even have the data structures that source code is made of in Common Lisp and its antecedents, then there is a nontrivial sense in which it's not a Lisp--or at least not the kind of Lisp that those older ones are.