With a little searching of various questions on Google, I found a way. It may not be the best way and it may be over complicated, but it should work and that's the main thing. Though, if you know a better way or can find one, please do let me know!
I found that you can deploy your code to your servers via Git hooks. All you need to do is SSH into your server, create a git repo and then set up a hook for you to push commits to this repo. This will allow you to push your commits to your servers, but has nothing to do with gitlab at this point.
The next step is to add the push url for gitlab to the same remote. This way, you will be pushing to both gitlab and the site itself each time. As a result, both the gitlab repo and the actual site will both be in sync. Though this is a hack and is definitely not efficient.
I found how to deploy your code to your servers via git from this blog post: http://sebduggan.com/blog/deploy-your-website-changes-using-git/
I found that you could add two push urls to your remotes in git from this question on stackoverflow: http://stackoverflow.com/questions/14290113/git-pushing-code-to-two-remoteshttps://stackoverflow.com/questions/14290113/git-pushing-code-to-two-remotes
As I said, if you can find a better way, please do let me know. This will work, but it means having two versions of the same code. Of course, this is very messy and is a big waste of your server's storage.