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I've read pretty much every community/help page for this problem that's specifically related to Steam (no one else seems to have reported the same issue here in GoG), but none of those fixes - Windows XP compatiblity mode, run as administrator - apply to/work for me, as GoG installed the game with those switches already ticked. I've attempted to "Verify/Repair Installation" several times, with no success.

Any help would be greatly appreciated, as I'm at something of a loss.
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I honestly can't recall anyone ever having this particular issue before. (And I've been part of the game's fan community since the beginning.)

Since you said you checked the Lithtech.exe compatibility settings: that means it isn't missing from the TRON 2.0 folder, for some reason.

And the game still works fine on the most recent Fall Creators update for Windows 10, so the version of Windows you're running should be irrelevant.

So, apart from that . . . one of the few possibilities I can think of right now, is perhaps an anti-virus/anti-malware/firewall, or some other process running in the background, is blocking Lithtech.exe from executing. (Which is absurd, of course. Since this version of the game doesn't even have any DRM, that a security program might get a false positive result from. But I'd check, anyway.)

As a last resort, you can always install the Unofficial Patch for the game. Which might help, since it replaces the game's executables with more up to date versions. There's a link to a page where you can download it, in this topic.