The game probably requires a pass through from steam login to auth the players and server. ie you need an internet connection.. however, it might be possible to setup using the file directly..dunno, not tried using it on lan.

It is odd you get disco'd if steam goes down.. or do you literally mean your isp? Could try running steam in offline mode.. see if you can get it to connect to lan.. if it doesn't.. you'll need steam to be online.