Quite a few reasons.
1. UDP packets can be lost in transit on the internet, and this doesn't happen via LAN. UDP also doesn't require an active connection, so you don't need to specify a specific computer to connect to. LAN approach does a generic broadcast, and computers on the network can respond. You can't broadcast to the internet.
2. UDP support of the actual game server is irrelevant. It's an option, and has nothing to do with the lobby server. So yes, you can.
3. Everything persistent. So if you create a channel with its persistent flag set to 'true', then all of the persistent RFCs you send there (Target.AllSaved, Target.OthersSaved), as well as all created/destroyed objects will be recorded and saved into that file. So the next time you join this channel, you will go right back to the state you left it in.