1. Double check this
Setting up Java 1.5
2. If still problems, download the Java 1.5 again from apple getting the "Offline" standalone java installer.
3. Delete the LW prefs folder found here: /Users/your_username/Library/Preferences/LimeWire
4. Check your graphic settings.
5. Make sure you have plenty of ram. 500+ MB is best.
6. Do these maintenance routines:
SAFE Boot & Repair Permissions
7. Try step 8 here
Can't launch LW: Bouncing in Dock (click on link)