I've read that Litespeed is alot faster than apache. I use mostly wordpress and joomla sites and am looking for a new server. Will i see a significant increase in speed of wordpress being on a litespeed server?
No you will not see a significant increase in speed just by being on a litespeed server. They claim it serves PHP 50% faster (than mod_php) but they haven't updated their SAPI in over a year. PHP-FPM will blow it out of the water any day.
Stick with open source and if you want a web server that really is faster take a look Nginx
Sorry if I go a little bit off topic here, but I just wanted to comment on this subject, maybe most of the things you already know.
When you want to speed up the wordpress site there are a few steps you can take that will make an major difference.
One of the things is cashing. Wordpress has great plugins that will help you with minifying and caching your cent.
Another major difference will be a CDN. You can things as Amazons S3 and cloudflare to distribute your static files all accross the world. This will increase the speed of your website dramatically.
If that is still not enough than you can resort to measures as changing from http servers. Now I can not tell you a lot about litespeed, but I do have some experience with nginx. But I think they will perform almost the same.
From my experience nginx is a little faster than apache, I had the exact same wordpress site on two servers, and nginx did a lot better than apache. I read that it had something to do with the way nginx spawns the processes, but that is a topic for ServerFault.
To conclude, changing your http server can make a difference, but be sure to have your site optimized before switching.