Has anyone had any luck playing this over multi-player LAN? Does it require multiple purchases of the game or can you install it on more than one PC at a time? I can't seem to get LAN to work for the life of me! I have change my firewall settings appropriately and even turned it off at one point. Thanks in advance!

Try GameRanger - http://www.gameranger.com/

As for multiple purchases - AFAIK it doesn't come with the serial key, so one copy should be enough for multiplayer, as you can install it on unlimited number of PCs in your household.

I have had no problems with LAN play at all. The GOG version also works well with the original CD version of Galactic Battlegrounds Saga. I would ensure that the proper ports are forwarded in the LAN router, as well as the ports being open on the individual computers' firewalls. Also, older games like Galactic Battlegrounds use DirectPlay components inherent to DirectX that may need extra port forwarding.

I had some initial connectivity issues on lan, but I looked at the support page on gog for this game, and their solution worked for me.