Are you running Java 1.5 or 1.4? Go to the Utilities folder & open the Java > J2SE 5.0 > Preferences & make sure Java 1.5 is selected. It's described here
Setting up Java 1.5
You could also try deleting your LW prefs folder found here: /Users/your_username/Library/Preferences/LimeWire
But that would mean you'd need to reset all your LW options if you can open it.