As far as I know, the Litespeed cache does not directly interact with any software and Xenforo would not be aware that Litespeed is caching things. You need to have a paid Enterprise license for Litespeed in order to enable the cache. Instructions can be found here: http://www.litespeedtech.com/support/wiki/doku.php?id=litespeed_wiki:litespeed:cache
The license of LiteSpeed I already have registered, which I am interested in the cache of the pages is compiled for the the pre visitors, and is used in Vurnish + Vbulletin