After upgrading my system a couple of days ago, League wouldn't start at all via Lutris. After some experimenting it started again if I ran the Riot Client from the "run exe inside wine prefix". It turned out that the latest release of "gamescope" (which I use because otherwise my mouse escapes to my second screen on Wayland) is broken. Reverting to a previous version via the arch package archive fixed the issue and League starts without problems.