Live Mesh is LAN aware, but it still requires a connection to the Live Desktop and the Live Mesh service. The Live Mesh team is working to enhance the Peer to Peer sync process, so it would be good for you to add your voice on the issue by voting on the suggestions (or filing a new one) as described here:
Live Mesh Beta: Suggestions - Go cast your vote!
-steve
Microsoft MVP Windows Live / Windows Live OneCare & Live Mesh Forum Moderator