I just accessed GH with my mobile phone and i had no problems with any lag of any kind.
The most likely reason is probably that your phone is not powerful enough or too old to render this website.
Unless there is some magical XenForo "addon" that adds mobile functionality the problem is gonna be that we cannot mobile optimize because we do not have the power.
In order to tackle the "lag" issue on older phones like some websites ( youtube/facebook does) We would need to create an entirely new website format just for mobile phones that renders far less on the screen, that would take a lot of time especially since we would have to port the forum functions over to the "mobile" forum, it would take a very long time to port everything over and rewrite it as a mobile website, especially if you are only one person doing it (like Xyphien). There is also the problem with Databases and that kind of stuff.
I just loaded it up on my phone as well, it's a bit slow, but that's because of my internet. Everything runs fine, and it is in fact mobile friendly on my end. The main header/banner is uneven, but that's nothing too big. You have all the functions, and it forms with your phone will little issues (The footer is another weird looking thing). I did just add ForumRunner functionality, so if you'd like to download the app ForumRunner and use it to navigate GameHandout, it might run smoother.
or maybe it's in the browser or ram.Butt (*coughs*) I mean But when I use browser on sites like facebook, steam, some social media sites and other forums it does not lag Plus I tried it on 3 phones with different android versions still got the same thing it's like press a letter 5 secs to enter that's why my Thread here is short