I have heard Apple will be releasing their Java 1.6 for Leopard soonish. They have a beta version of it out now apparently.

In the meantime, there's things you can try. Can't launch LW: Bouncing in Dock (click on link), although some of those things will obviously not apply to the new OSX.

I don't know if Leopard also includes Java 1.4.2 as did Tiger, but if it does, you could jump back to LW 4.12.16 & set Java 1.4 as the java for java apps to use in the meantime. Setting up Java 1.5. I would recommend deleting your LW prefs folder however if you did attempt this. It's found here: /Users/your_username/Library/Preferences/LimeWire
At the bottom of the page of the first link I gave is a sample image showing how to do.