Since this happens to you often, I'd strongly recommend ruling out hardware issues. First, check you RAM with Memtest86 or similiar tool for a few runs. Bad RAM will eventually corrupt your file system, so do it before you lose any important data. Then check your storage health, and while at it, if your games are not installed on a ext4 file system, make sure you create one for testing. Last, make sure you have enough space on your game library partition.

Next, gather data. Are the games that fail windows or native titles? Wine sometimes crashes and leaves processes running and running the application again fails. Check with 'ps' command or your favorite GUI tool. Check the logs of your game launcher, wine and the game it self. System log aka journal may have some info too. Journal is unlikely to have useful info in this case, but still it's worth to take a look incase it's some wierd issue with network, GPU, etc.

Lutris forums have troubleshooting section. There is a sticky post "Please read before asking for help", that covers the details about logs. Other threads there will be good sources to learn.

I hope you're able to fix your issue.