So long as none of your friends take the game home with them, you're in the clear.  Chances are if you're not pirating (that is, no one else is going home with the game) neither the devs or publisher has a problem with what you're doing.

But is it possible?  I have no problem with it ethically, since my LAN parties usually cause people to go buy whatever game we played, so they won't get their butt kicked at the next LAN party.

I ask because the manual says that you can play on "up to two connnected machines using the same serial number".  If it's not possible, I'd like to know ahead of time, so we can decide if someone is willing to buy another copy or if we need to play something else entirely.

I'll be concise - has anyone played 1.81 Sins, or better yet Entrenchment on more than two machines locally with a single key?

I play Sins mainly, but I have a copy on my brother's computer as well, and sometimes he'll play a LAN game with me. I also have a copy on my laptop.

It works fine. I play LAN with my roommate all the time. I actually have let people install it to play LAN parties and they end up buying it (a la baens free library style). So no worries Devs, all I have done is get you new customers.