You don’t need to install wine. In Lutris you should set the wine version to the latest proton-ge (that’s a wine fork for gaming). And also did you install the game via Lutris or wine? You should install it via lutris. I just did it once with a pirated game (NFS Most Wanted) and it worked just fine.
PSA you can download a savegame with a city pop of 100k to check how well the game will run in later stages. By doing this you can check it and refund it if necessary.