Another problem that I have is, I think, because main menu is hidden on checkout page, from time to time, menu also disappears on home page. And I have to flush litespeed cache in order to make it appear again.
LSCPS works with warehouse themes and panda themes. It may or may not work with your themes. You can check with the theme developer, or module developer for classic Cookies Banner to check more on why it doesn't work. This module may not be cache-friendly and can not retrieve some variables from cached pages.