Hey !
I bought a game on steam, but I cannot install it on lutris as it's not even listed...
It's a windows only game. Is there a way to play it? Am I doing something wrong?
If you don't see your windows games in steam on Linux you have to enable Settings/Compatibility/'Enable Steam Play for all other titles', then just install normally from the Library screen.
I want to add, for OP and others' sake, that you don't need to add all of your Steam games to Lutris/Heroic/whatever in order to play them. This step (enabling Proton) is all you should need.
I would also like to add that if the newest Proton version doesn't work for a newer game, you should grab ProtonUp-QT. Sometimes GEProton will work or else come out with support faster than official channels.
Install Steam client, log in and download it there. Even if you connect Lutris to you Steam account, AFAIK, the way Lutris launches those is just launching Steam