I suspect you mean WWW::Mechanize not LWP::Mechanize. The answer to Is this possible? is of course. You can do anything with Perl you like through a CGI interface. There are differences in the way permissions and data exchange happen but you could easily use a CGI to take parameters to make Mech requests and return the results to the browser however you like. Your question as it stands is awfully broad, though, and that's probably why you're not getting answers to your post.

If you want to take a stab at a Mech request inside a CGI, or just a basic "hello world" CGI for starters, and come back for more, there are hundreds of links and posts here about how to do CGI. Try some super searches or tack a "site:perlmonks.com" onto a Google search.