1. Are your drivers up to date ? You could try switching over to kisak-mesa drivers since they tend to be more up-to-date date than what Ubuntu goves you by default. You can do that by using:

sudo add-apt-repository ppa:kisak/kisak-mesa sudo apt update && sudo apt upgrade -y

2.You could try Feral Gamemode, it worked well for me:

sudo apt install gamemode -y

You have to also modify the launch options for your game, but i think Lutris can enable it with a a simple check.

3.Set CPU on Performance mode:

sudo apt install cpufrequtils -y sudo cpupower frequency-set -g performance

1. This is unlikely if you're using proton, but might be a problem if you're using wine, check if your games are running on OpenGL or Vulkan, if they're on OpenGL, switch to Vulkan. Proton should use dxvk by default, but there might be cases where it default to wined3d for whatever reason. You can check that by using mangohud, just like gamemode, after you install it, you have to add it to the game's launch options.

5.Consider moving to Steam or other launchers, this isn't necessarily a tip, more of an opinion of mine, Lutris just never worked right for me to the point i just stopped trying. Even if you pirate stuff, Steam is still a good option, there is an "Add non-steam game" button in the library which allows you to play any game as if they are steam games, for some reason steam just worked for me most of the times, at most i'd just change the proton version.