1. Install the game of your choice on Steam and get it running.
2. Download Mod Organizer 2 (.7z instead of .exe) from GitHub and extract it, preferably on the same drive as your Steam instance where the game is located.
3. In Lutris, press the '+' which is located at the top left corner of the screen. A pop up box with some options will appear.
4. Select 'Add locally installed game'
5. In the 'Game info' tab, name your game and select 'Wine (Runs Windows games)' from the 'Runner' drop down list.
6. In the 'Game options' tab, navigate to where your ModOrganizer.exe is located and choose it for the executable, then select the game's Steam prefix folder as the wine prefix. This can be found in /Steam/steamapps/compatata/. Your game's folder is usually the same as its Steam ID (i.e. Skyrim is '489840') but if you're unsure you can refer to the next step.
7. Download Protontricks and run it. A list of detected games will be presented alongside their wine prefix folders, select the game, then select 'Install a Windows DLL or component' and download and install vcrun2022 inside it, which is necessary for MO2 to run.
8. Now you should be able to select the game entry in Lutris and run it. When it runs, Mod Organizer will start and you can configure and run the game from there.
You must run Mod Organizer 2 for every game that you want to manage. To do this, you only need one portable instance of MO2 (i.e. zip folder as opposed to installing via executable), because when you provide the Lutris entry the managed game's wine prefix folder, it will automatically create a new instance for that folder. In other words, you can use the same MO2 executable with different wine prefix folders, and in this way you'll have different instances per game.