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I looked in the PCGamingWiki, but the save file location for the GOG version is not listed there.
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Any update on this?
If you're just looking to start over a fresh game, you can reset progress from the options menu.

If you want to backup your save or move it for some reason, go to the games directory then Lus_Data>Save.
There are files there for progress, story and settings; not sure what each does other than settings though.