By far the best quality site for competitive programming at which you can use Common Lisp is AtCoder. It provides most problems from rated contests in English. A drawback is, however, that no English editorial is provided for beginner contests. Other famous and international sites include CodeChef, CS Academy, HackerRank, HackerEarth, and Kattis.
You can see other people's submissions in most sites. (Exceptions include Kattis.)
Most sites provide an online test environment: e.g. here at CodeChef.
As far as I know, only code-chef and spoj support common-lisp. And both of them return
NZEC
, when I submit solutions in common-lisp. Any suggestions?