With Proton 3.16-6, all I had to do was download this dll https://github.com/AccountOneOff/lutris_files/raw/master/xlive.dll and put it in the folder "GTAIV" which you can find in the root directory of the game. That's it, nothing else. You don't have to create any online accounts, just hit "play" button when small window pops up when you launch the game. The game saves locally just fine.

Speaking of game performance, it runs at 30-50 fps with disabled shadows, which is good if you really want to play this game. Tweaking other graphics settings doesn't seem to change anything. Everything is on high (except shadows, of course)

(sorry if there was typos)