There is no such way to disable cache for a module. only by URLs. on the other hand, LiteSpeed cache doesn't cache shoppting cart at all. You should check header and there should not be any cache hit header. If so, it deosn't seem LiteSpeed cache plugin related issue, rather than your mobile module issue.
I mean there is no configuration to disable cache for a module directly. If you modify the Prestashop PHP code, then that is a different story.
You can share back your solution in more details about your case and others will benefit from your solution.