Forget Lutris, just use heroic game launcher. Click Add game, select the battle net installer exe, run it and let it install, close it then switch the path to the installed battle net exe. Heroic will use proton ge (i believe by default) and it’s worked for me without issue. I tried lutris first because that’s what showed up online when I searched and I had nothing but issues. Then I did it in steam, with similar steps to what I described already and I could get it to work, but in heroic it was just a couple minutes and it’s good to go.