Hi,
Well, for starters I would suggest making sure you are using the index table engine, it should be a bit faster even when using the filters. I assume the LiteSpeed cache has it’s own object and page cache, which is probably used when doing these searches.
There is however an internal cache option as well for the plugin, which you can enable here: https://i.imgur.com/hak7iW7.png
This can not be pre-filled, because of the large amount of possibilities, but if you choose a large enough number for the cache interval (I usually suggest 10 days or so – 14400), then it should slowly but surely fill up.
