SOLVED is Civicrm compatible with Litespeed technology?
I am using the webhosting service of Rochen, and they use a LiteSpeed Web Server.
Civicrm runs inside a Joomla 3.7.5 website quit okay. (The the current Joomla version of 3.8.2 and Civicrm do not work together okay, because there are still several issues due to changes in the Joomla 3.8.* versions.)

So as to your main question: Litespeed can be setup to accommodate Civicrm.