See, I have a few friends coming over for a LAN party, and I want a game to play together, but I'm a poor student. Is it possible to use the GOG copy of the game to play together on LAN? It's really not possible for us to shell out the money needed for 6 copies and we only want to play it for one night. In addition, I'm not going to share the game with the friends, and I'll delete it after the night.

I'm more concerned with technical feasibility, rather than legal feasibility, since I live out of US jurisdiction in a country that doesn't tend to prosecute such crimes. I've nothing but respect for the creators of Project Zomboid, but financially, I don't have the money to purchase 6 copies, and I think that playing a single night with friends, would fall under the "watching movies together" metaphor outlined in GOG's FAQ.

Can you do it?

Based of clarification from the one who posted this question

Yes, the game is DRM free so from a technical standpoint you can do whatever you want with it!

Specifically what you want to do is use the in-game Hosts function. It should be as easy as plugging in the IP address.

The in-game Hosts function should still work. The host will just need
to provide their IP to those that want to connect.

Port 16261 might have to be forwarded as UDP and opened on the host's
firewall.

You can read more here

As you mentioned copyright protection does not apply in your country so you may do whatever you wish with the software.

Legally speaking for the rest of the world it's a complicated question. It could be argued that it's legal to make copies on your own system also legal for you to borrow your friends computer one night and install it for that one night only (if you delete it before they leave your house.)

While the game itself may be free of DRM, GOG.COM policies do not allow it

Can I enjoy my purchases both on my laptop and desktop computer at
home?

Yes. We do not limit the number of installations or reinstallations,
as long as you install your purchased games on computers in your
household. So yeah, if you've got a render-farm in the basement, you
might actually break the world record for the number of legal Witcher
installations in one household. However, if you think about installing
your game on a friend's machine or sharing it with others then please
don't do it, okay? The same principle applies to movies - you're free
to watch them anywhere you want, with anyone you want, as long as you
don't share them with people who haven't purchased them.

Emphasis mine