If there wasn't a demo when the game was originally out, there won't be one here. I know there's a demo thread somewhere with links to preexisting demos, but that's it.

Here.

Just about everything is going to play better off of GOG seeing as they actually make sure the games run properly on modern machines unlike steam.

Valve patches its own products, and distributes patches made for other products, so it's not like they're all bad. If, however, you meant to say, "the administrators of Steam do not take personal responsibility for making sure that every one of the games they sell works properly whether the manufacturer issued a patch or not," then I'd have to admit you're right.

It's a shame that there aren't any GOG demos, but i understand why not. It'd probably be a real pain to try and debug the demos as well as the games, in many cases it'd double their workload.
But, while some nice guys on the forum have put together a huge list of demos for gog games, it does mean there's really no way to check the compatibility on your PC, as those demos won't have any fixes implemented.
Eg: I tried the Unreal demo and it was horrendous and unplayable on my PC, but i'm assuming the GOG version is nothing like that.
Anything on DOSBOX (any old dos game) should be fine. Otherwise, your best bet is to quickly check the game's forum before you buy. there seem to be a few issues with TLG, but i don't know how widespread they are.

How on earth could this be true? Does GoG somehow have the special ultra-secret HD-version of TLJ?
Anyway, you won't see a possible performance increase in a demo since it is not patched like the full game, as mentioned above.

There is a better looking anti-aliased version of the game. But judging from the screenshots, GOG doesn't have it either.

Yes, feel free to favourite our demo thread.