1. Check under Apple icon top left of screen for Software Update ... see if there are any system updates waiting.

2. I'd suggest you do a Safe Boot & Repair permissions. Hold down SHIFT key whilst your computer is booting until you see the apple icon. Then log in. Then open Disk Utility, select the OSX drive on left & choose Repair Permissions. Then reboot normally & try LW again.
Repair permissions should normally be done after any system updates, however might be wise after any adobe updates also such as flash.

3. An idea might be to check if the problem is account related. Set up a temporary test account & see if LW runs from there: Setting up a Test Account in OSX (click on link). You can easily delete this account later, doing such removes all support folders & files for the second account.

4. One option that usually works is one which is harder work. It means reinstalling MacOSX from the installation disks. This means a clean install which deletes all other data on the drive. Obviously you would need to backup all personal files, any installer programs downloaded, etc. Obviously this option is the less inviting one, but always seems to fix the issue. I believe the issue is an issue with the original java installation.