installed Page Speed ... hmm, are the advice from Page Speed->Performance->Analyze Performance?
Now I think I've got clear about this "Vary:Accept-Encoding" issue. It should be automatically added by litespeed when the page is compressed. please check the response header, if "Content-Encoding:gzip" is there. This is important for performance. Please post any 1 page's all response headers here for us to check it together.