Is there any video-chat-via-LAN application that doesn't require an Internet connection?
To install, press Ctrl+Alt+T on your keyboard to open Terminal. When it opens, run the command below.
Not sure, but I have read about some jabber servers with videochat support.
May be, the Openfire jabber server includes support for video.
Have a look at this, too:
In this site, they say that using a Red5 plugin, the jabber server supports videochat.