Very difficult. You can try by asking one of the network technicians about the possibility & any ways around it (such as opening up port 6346 or/& making exceptions to Limewire to the app list.) The newest beta version (LW 4.3) released today is supposed to make it easier connecting thru firewalls & will soon be released as LW 4.4 (as soon as they're happy with it & added a couple more things.) Go to the LW Beta Program section to find out more.

Other things you can try is:
1. Force IP: Force IP instructions & sample image
2. Try a different port number to connect thru (see LW's Prefs>Advanced>Port & pressing Apply after any changes.)
3. Try the Jum Build