Litespeed and LSCache make a pretty powerful server combination that exceeds anything that Apache could ever do on its own.
Litespeed handles incoming requests faster then Apache.
It handles SSL handshakes faster then Apache.
It can increase PHP performance by almost 50% due to LSPHP(lsapi).
It provides features that Apache doesn't have too, such as it's own internal WAF(Website Application Firewall) -- it's really hard to justify not having it.
While it can increase page responsiveness and decrease speed/load times there are other configurations that can be done to a website to help, such as expiration headers, brotli/gzip compression -- these can all increase pagespeed ratings.
I do believe you'll see a decent increase, but I don't want to guarantee. Mileage does vary but in my experience most users see a decent difference..
A higher tiered VPS package is always going to provide more resources at your disposal to handle increased traffic but Litespeed handles traffic better to get more out of lesser packages. Unfortunately, some websites will require both -- a way to gauge is to look at your recent usage in system resources if you're able to view this. Typically requires SSH access at the root level.
Ultimately, it never hurts to have both especially when running a forum related software like vBulletin.