I love that the games here are DRM free. Now, my question:
Is it possible to LAN this game with just free versions?
More specifically, would I be able to host a LAN DayZ server without my friends having unique codes?

I would love to LAN this game with a single GOG copy. If possible, reference another post that may have answered this already. I browsed over the names of topics and viewed ones that I felt would be relevent but found nothing this specific.

Thanks in advance!

I'm not sure if the Day Z mod can be run over a LAN, I remember seeing a post on the day z forums and someone said it uses an external internet server for stats or something, but I'm not 100% sure since i've never played the dayz mod myself. I run arma 2 over a LAN and it should be possible to do the same with the free version but there are some limits like lower quality graphics, cant run user mods and no campaigns (source: official website).

I suspect that the no user mods part refers to actual mods as opposed to user missions, if so there is a mission called dynamic zombie sandbox which is probably like day Z (like I said I haven't tried dayz)

One last thing, you may need to run your mission on a dedicated server, it sounds complicated but it can be run right out of the box although there is probably some kind of LAN only option like sv_lan 1 from valve's source engine.
There is also a config guide floating around somewhere which tells you how to adjust the server. if you don't create a config then everyone joins the server and can vote for an admin/mission

I hope this information is useful and relevant, since i've never used either arma2 free of dayz I can't be 100% sure but good luck all the same