As far as I am reading, LiteSpeed fully supports Apache mod_rewrite rules and .htaccess files.
With that in mind, you will notice there is a htaccess.txt file in the root of your XF installation.
Rename this to .htaccess
In XenForo > Admin CP > Options > Search Engine Optimisation : Set Full Friendly URLs to On.
If this doesn't work, change it back to Off and rename the .htaccess file to htaccess.txt