I haven’t used Ubuntu, but I had a similar setup to yours in the past, and on Archlinux I couldn’t run any game until I installed 32 bit nvidia drivers (on arch the package was named lib32-nvidia-utils), and that’s my first instinct - maybe you don’t have 32 bit drivers installed?
Now, as I haven’t used Ubuntu much I’m just going off of online reference so there commands might not be 100% correct, but try doing this:
sudo dpkg --add-architecture i386 to add 32-bit app support
sudo apt install -y libvulkan1 libvulkan1:i386 to install the vulkan drivers, including the 32 bit one. I’m not sure if this will have the same effect as lib32-nvidia-utils package on Arch though or if it does the same thing, but hopefully it works.
As for League, it does work on Linux quite well, but the installation is a little bit unusual. The gameplay though is literally the same as on Windows, no performance loss there at least in my experience.