I want to know if the Enterprise 1CPU-Core license is valid for use on a VPS. Do you think that it is a good idea to install Litespeed on my 2GB RAM VPS (http://www.rapidxen.com/getPlansServlet)?
You can run Litespeed on RapidXen's lowest VPS plan if anything... It all comes down to how much traffic you are getting and what specifically you are hosting.
The VPS plan you have should be as powerful as a dedicated server, so it's definently appropriate machine to run Litespeed.
Don't mind it being 1 CPU license, your server will still use the second core for processing php (if you use it) and other stuff.