1. Make sure you have all OSX updates by going to Apple menu -> Software Update ...
Software Update
2. Do safe boot repair permissions:
SAFE Boot & Repair Permissions
3. Make sure Java 6 is up near or at top of list in Java preferences:
Setting up Java for Leopard (see 2nd image)
4. Try opening LW again.
5. If not good, see if LW works in a different account:
Setting up a Test Account in OSX (click on link)