Litespeed is the webserver, Cloudlinux is an operating system. cPanel comes with Apache installed by default. If you're looking at a more efficient server and a cost effective solution, then yes, you should try nginx. There's at least 2 plugins for cPanel out there that can assist in automating the nginx installation. One of them is free, the other paid. I think they're: http://nginxcp.com/ http://cpnginx.com/
Yeah, the irony in their names
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Until you expect more traffic or load on the server, nginx is not necessary to run your VPS fine. Nginx is faster to serve static contents and it will give you a performance benefit with moderate + high traffic servers. But with the suggested plguins, it will give you an an additional layer of administration effort with no gain if your VPS is low traffic one. Also there is one more plugin offering Nginx ( direct server or reverse proxy )+ PHPFPM on cPanel servers, which is cpxstack.