Crawl as logged in user

Can cache be generated for logged in users? There is such a solution in the wordpress or magento module.

I'm not 100% sure but I think all logged users share the same cache and just the ESI stuff is different. I don't think a separate cache(product, category, etc) for every single page and for every single user is generated as it is partially pointless and just too much for the server I guess.
Yeah, I mean to use the litespeed crawler to crawl the website as a logged in user.

Otherwise I'm aware of the option you said, but I'm looking to have different price for logged in users...