You're looking at the problem from the wrong angle. The question is not if Q2A supports Litespeed, but if Litespeed supports PHP (the language in which Q2A is implemented).
The structure looks like this:
Litespeed is the webserver, PHP is the runtime environment, and Question2Answer is an application.
But to answer your question: yes, apparently Litespeed works with PHP, so it should support Q2A. It looks like you need to install a specific version that is precompiled with PHP support, though.