Do I need two licenses to play StarCraft 2 multiplayer over a LAN?
Starcraft 2 does not support LAN, so yes you'd need two licenses, but you'd be playing over Battle.net NOT lan.
You will need to be able to connect to Battle.net. You can give your friend a 14 day guest pass from your account. He should be able to play on that.
There is no LAN in SC2 (yet), only internet. Consider your LAN mates as arbitrary internet players. Each connects to Battle.Net, authenticates and plays connected to the internet.
So, yes, each one will need a separate Battle.Net account and a game license.