Lutris settings: Add Game -> Name (sth you want), Runner Wine, Release year 2022 -> game options -> Executable (.exe file of bbpsx), working dir WindowsNoEditor directory, prefix architecture 64bit -> save
There is an additional step:
WINEPREFIX=/mnt/gamedrive/mywineprefix winetricks dotnet35
If you don't do this before launching it, the game will refuse to start. Obviously replace WINEPREFIX according to the path on your system.
Also, I'm using wine-custom-ge (aka lutris-ge) 6.21-1. I had some weird errors on Wine 7.0 staging