Hi
lazlot,
If this is a control panel server, you can easily switch web server and test the speed by some benchmark tool, e.g. ab, h2load..etc. on the other server.
If this is a stand along server, you can setup port offset on either LSWS or Apache, also, be sure that both php parameters/modules as much similar as possible.
What kind of page or application going to be tested? WordPress site?
Welcome to join LiteSpeed community
https://goo.gl/FG9S4N
Best,