FWIW My host is Lightning Base, which uses LiteSpeed servers; although LB is essentially a WP specialist, they do host CP sites. I have encountered no problems (of which I am aware), though I use a very basic LiteSpeed Cache setup.
Thank you Tim and Doug. We use LiteSpeed Cache for our clients on LiteSpeed servers (as Doug mentions). Although we don’t run LiteSpeed on our server, it may make sense to use with CP as it is supported. Plus can use it to hookup to the CDN.
Cheers