Home LANs and The All Seeing Eye (ASE)
ASE shows people a game that is online at the time and the IP it is at. When you have 2 or more computers hooked up on a home network and one is connected to the internet with a router the gateway pc will broadcast that it is online, and it is in fact hosting the game to ASE.
Without seeing a home LAN on a LAN list you can still join the cable IP if known. This allows you to join a home network and play with them.
If you are wanting to play a private LAN game on a home network you must disconnect the gateway computer from the router or pull the cable/phoneline depending on which kind of connection you have or just turn the router off.