Someone on the Steam Deck reddit did a PSA on this as well. It isn't just Lutris. It's happening no matter how you install Battle.net. I am getting this issue when installing Battle.net straight through Steam as well. Don't continue to attempt to update, this will create a bunch of temporary files in your install directory and some people have said it might even corrupt your prefix. Just wait a bit while it all gets sorted out.

If you're having trouble with Lutris you could always try adding Battle.net into Steam as a Non-Steam game and set the compatibility option to use Proton.

I've been running it this way for months now and play D2R and D4