No.
Lisp-N has to do with the number of name spaces in the language. Lisp-1s only have ONE environment; the variables range over all values of the language, integers, functions, vectors, symbols, strings. In Lisp-N, there are N namespaces for each "kind" of value.
Common Lisp is called a "Lisp-2" because it separates functions from other values. (it's closer to Lisp-5 or even Lisp-7, forgot which, because it allows that many kinds of "names" without collission.
Also above you said Clojure "probably" has better data structures than Common Lisp. That is unsubstantiated.