If all your games are available in Steam, I see no advantage in using Lutris: in my experience, Proton works very well out of the box.
For games that aren't available in Steam, Proton is of little help AFAIK, and that's where Lutris shines.
Also, some people like having all their games in a single place, in which case Lutris may be a solution too, even for Steam games. As my “single place for games” is my shell, I usually skip Lutris and Steam GUIs to start games directly anyway, so…
