I just upgraded to Lion yesterday. Went to open Vuze, said I needed to download Java. Did all that, and like everyone else no incoming/outgoing traffic at all. So on doing a search I came across this fix and can confirm it works.
Change your jar file:
1) Go here
http://dev.vuze.com/ Download the development build jar file at the top, its named Azureus4605-B13.jar
2) Once its downloaded rename it Azureus2.jar
3) Go into applications > vuze > right click and "show package contents"
4) Open the contents folder > resources > Java
5) Delete the Azureus2.jar file found there and replace with the one you just downloaded and renamed as the same
Make a backup of the original Azureus2.jar file just in case. I did before I deleted it just to be on the safe side.
Happy Vuze'ing