Well what version of unity do you have ? Second if you think a light weight desktop enviroment will make your game run faster than, you can install the Lubuntu xubuntu environment inside ubuntu. Lubuntu is the most light weight. You can use their environment instead of unity. However, unity will still be on the system, just not in use.
I currently have xubuntu (second lightest weight) , and am running it alongside unity, which is unstable, but really beautiful. If you prefer completely getting rid of unity and want to run the LXDE desktop,you’ll have to do some extra steps.
Try as many as you want.
Different environments commands
sudo apt-get install ubuntu-desktop
sudo apt-get install kubuntu-desktop
sudo apt-get install xubuntu-desktop
sudo apt-get install Lubuntu-desktop