I’ve been running the EA app through Lutris as just a regular program and it works “fine”, Sometimes it crashes on launch but all games I’ve played through it from Battlefield to Titanfall 2 have worked.
Funnily one of the things that got me to try Linux was the EA App randomly stopped working on my Win10 install. Seriously how has EA kept their desktop client such a buggy messes after all this time? Origin was a load of crap but I still had less issues overall with it.