The 2 things I'd suggest are:
1. Try deleting the Limewire preferences whilst LW's closed. The file is found here: /Users/your_username/Library/Preferences/LimeWire
2. If that doesn't do the trick, re-install Java but "only" using the "Offline" standalone Java installer.
Java 1.4.2 for Tiger (click on link) I think is the newest one. However, if you're using Java 1.5 then get it here
http://developer.apple.com/java/download/
Did you see the note about Tiger Java 1.5 & how to make LW use it? See it near the bottom of the page here
Major Topics for General OSX Help (click on link)