I have a laptop with an external monitor. My problem is that games won’t launch when I have the monitor connected to the laptop. I just want to have the game running on the laptop screen and Glances running on the external screen to monitor resources but to do that I have to disconnect the external monitor, launch the game and then connect the monitor back again.
Have you tried tweaking the configs? There are a couple of advanced settings under “System Options” tab that might help, including turning off monitors - although I have no idea what Lutris uses for this.
Failing that, you can set up a script to temporarily disable monitors yourself using xrandr or similar, launch Lutris, run the game, and then revert the monitors on exit. It’s better than messing with cables