First of all, if your firewall can't be disabled or altered by any means, you have a very bad firewall. If you are serious about playing JJ2 (or any online games, for that matter), you will have to make some changes to the firewall settings.

As far as I know, none of the online launchers support LAN play directly. However, all you need to do is host a game with a launcher, and then for the people in your network who want to play, instead of choosing your server in the server list, they should just enter the local (192.168.x.x) IP. This will allow everyone on the LAN to join the server, as well as let people from the internet play as well. If you don't want to have people from the internet playing (you want a private game), some launchers (I know XJJ2 does) have an option for disabling of listing in the server lists.

Could you give some more detail about your network? If you have a firewall program running on the local computer, the above solution will not work, but if you have a router or some other external firewall it will.