No fix, but here are a couple of possible workarounds:
 
Restart your machine in Safe Boot mode (hold down the shift key right after the startup tone), run Software Update again, then restart  normally. Java sometimes needs a few machine restarts to work properly after a new install. 
Create a new admin user account and install LW there.  
Get more info: run Applications/Utilities/Console and copy the readout when LW quits unexpectedly. Post the info here or in the developer's beta forum at 
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