If the game comes in an archive (like portable Windows applications), you can simply copy the files to a directory and point Lutris at the executable.

Compatibility has been pretty solid for me. There are only a few games that didn't work out of the box (excepting those that are intentionally broken through anti-cheat). You can often get away with running games on Wine, but for most games you'll want Proton. Lutris will detect and use Proton versions that are installed by Steam, copied manually into compatibilitytools.d, or it can download Wine and Proton releases on its own. There's also GloriousEggroll's fork with many game-specific fixes.

ProtonDB and Lutris.net are the most useful resources, you can check if the anti-cheat solution might be an issue on Are We Anti-Cheat Yet?, Steam forum is a thing that exists, and you can ask in this community.