Are you using Apache 2.0 mod_xslt? or using PHP's xslt functions?
LiteSpeed itself does not do xslt transformation yet, so you need to do it in PHP.
The xslt functions is not enabled in the prebuilt PHP binary, you need to built your own PHP binary, with --enable-xslt --with-xslt-sablotconfiguration options. Please follow our Howto to build PHP with fast cgi sapi.