I'm running via steam/proton, and I've encountered the situation you describe twice. Both times were after playing for several hours. Being difficult to reproduce, it hasn't bothered me much.
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When it happens during each session it gets a bit tiresome. Especially when progress wasn't being correctly saved. Had to redo a bunch of quest steps which gets old pretty quickly.
Installed directly via steam on X11 running buttery smooth here. Proton 8.0
Installed via Steam? You can't install Diablo via Steam can you? Just add it as a non steam game shortcut?
Works now though! It was just sucking up all my ram. :P
I have it installed through Lutris in the same way you have, running on Arch instead but that should make no difference really. I don't have those problems at the moment.
Perhaps your setting within Lutris are not right? Which version of proton are you running?
lutris-GE-Proton8-10, you?
additionally, if relevant, i'm running wayland and not x11
I'm on X11 so yeah, that's a diff.
lutris-GE-Proton8-7.
However I am using an AMD card, so I can't compare those settings to yours