First of all, you cannot play Diablo 3 or Starcraft 2 on a LAN. You are required to connect to Battle.net (be online). A lot of people disagree with this decision on Blizzard's part but it's the way the game is designed.
Secondly, as Ben said, you cannot "borrow" the game. But what you can do is get some Diablo 3 Guest Passes, which let you download and play the game for free within certain limits.
For Starcraft 2, you can actually just get the SC2 Starter Edition for free. Eventually Blizzard will probably do the same thing for Diablo 3, but for now you need to get a guest pass.