It seems you won't be playing Overwatch at a LAN party. While Blizzard are working on doing their best to minimise any ping issues, looking at regions and IPs, Overwatch will run exclusively on Blizzard servers.
This new information comes from Kotaku.au's recent interview with Jeff Kaplan and Geoff Goodman, who both have the same first name, but not. They also confirmed that there would be custom games in some form, although the details are a bit sketchy.
“We’ll allow you to set up some of those things that traditional dedicated servers allow you to do," they said. "Basically give you a safe place to go play a match to play with your friends and not go into the big matchmaking pool, we’ll have a setup that will allow for that as well.”
In the same interview, the pair also confirmed that there will be a spectator mode where you can jump into a friend's game - if there's a spare spectator slot - and float around the map watching the action unfold. Should have called it Overwatch Mode.