First of all you have to know is, that Pagespeed doesn't measure the loading time. It measures the "display time" after all data has been loaded from the server. LiteSpeed cache is speeding up the loading time, but not the display time, because only the php based main document is affected from caching but not static sources like .css or .js. These static sources and the way how the are loaded affect the display time Pagespeed is interested in. For Pagespeed it doesn't matter if a HTTP cache is used or not, because and again Pagespeed can't and doesn't measures the loading time.
If you allegedly have disabled caching for bots and if you get bad results now some other things must be wrong with your cache varies. Litespeed cache has almost no effect to Pagespeed.
Believe it or leave it....