It largely depends on the hardware.
It works very well with modern integrated Intel graphics, but it's possible you'll run into bugs or performance issues with AMD or Nvidia graphics.
As for installing, you'll probably want to add this repository for wine-staging:
https://github.com/wine-compholio/wine-staging/wiki/Installation#-ubuntulinux-mint
Then copy an existing LoL folder over to Ubuntu or run the official installer.
Lastly, you need to run a third-party tool once:
https://bitbucket.org/Xargoth/tuxlol/wiki/Home
It removes the mipmaps from all icons. Without it, the League client crashes when opening the item shop.