To say "Clojure doesn't run Lisp code" is to already assume Clojure is not a Lisp (else you would have to admit that it does run Lisp code: its own).
Take someone who is trained in Clojure programming and nothing else; which Lisp's code can they understand that is not derived from Clojure, like ClojureScript?
Basically, the criterion for a "dialect" is mutual intelligibility. A language which is an island isn't a dialect of anything. Two languages that are not mutually intelligible are not dialects.
Lisps are dialects which share a mutual intelligibility formed by the core that comes from the ancient Lisp. They are based on the same or very similar core concepts and use the same names for them.
That's not really a counter-argument by absurdity to my argument, as it's also valid.
To say "Swahili speakers don't understand English" indeed already assumes that Swahili is not a dialect of English. When one says "Swahili speakers don't understand English" they don't make an argument -- they make a statement of fact.
Now, one could argue that the fact that Swahili is different than English is well established, and needs no further arguments (as people will already be familiar with it and accept it).
But regarding whether Clojure is or is not a dialect of Lisp, I don't think that's the case.
It's not. Lisp code existed before Clojure.
If it can only run its own code, then it is no Lisp. Lisps share code.
I have a zillion lines of Lisp code. Then Clojure appears. It runs none of my zillion lines of Lisp and none will be directly translated to it (because it uses different data structures, has different operators, has different semantics, has different pragmatics). -> it's no Lisp
It's derived from or influenced by Lisp, that's it.
Like ML was derived from Lisp (it was originally even implemented in Lisp) and does not run any Lisp code. It's also no Lisp.
> Like ML was derived from Lisp
Like English was derived from Latin, French and Scots (among other things), yet is not Latin or French or Scots.
Like Romantic music was derived from Baroque, yet is not Baroque; or rock was derived from blues but isn't blues.
Etc.