The download from GOG uses ScummVM and not the original game engine.
The original game engine would not work well at all on modern computers with current versions of Windows.
If you buy the GOG version, plan to run the game on your modern computer, not the older one.
I don't know why installing Lighthouse would mess up the computer. The computer might be "too new" or "too fast" to run Lighthouse if it's a Pentium III, but I don't see why problems would extend beyond running that particular game.
I can't remember what computer I ran Lighthouse on, whether it was the 233mhz or the 400mhz computer. But both computers had Windows 98, and I patched the game to version 2.0a before running it. My game discs were version 2.0 of Lighthouse. Is it possible you have version 1.0 of Lighthouse? Maybe there are additional problems with version 1.0 ?