No. It's not possible. You'd need to be logged into the site to use LAN. If you have internet connection you can run a private server. Other than that... no.
Idk how LAN Parties work when using a game like this but I figure if everyone connected through the IP 127.0.0.1 (or other local IP) then you could get a fast connection to the server. But you'd still need to login on the site.
LAN is simple. You don't even have to have online-mode=false if you're PCs are connected to the internet. Just connect to your friend's computer. Either find the computer's IP, or connect to the computer name. If you guys are just connecting to LAN, no internet connection, then you'll need online-mode=false.