I assume you mean "Which modules like LWP can connect to a website through a proxy?" Well, LWP can. Using LWP::Simple, all you have to do is set the environment variable HTTP_PROXY to a value in a form like "http://proxy.domain.com:8080", and LWP::Simple will pick it up.

Alternatively, for more control, you can use some LWP::UserAgent methods, related to pxoies, directly, in LWP modules that allow direct access to it. That does, again, include LWP::Simple.

This is all documented in the section about proxies in lwpcook, the LWP Cookbook, and the section related to proxy attributes in LWP::UserAgent.