Hi
I had the same problem too, but found a way out... I suppose that you downloaded the 5.1.3 LW Pro version...

First of all, remove the install limewire.pkg from the receipts folder.

Second, the Java update should to be done again with the standalone update from the apple website http://www.apple.com/downloads/macos...05update4.html . Quit ALL apps before running the update. Reboot, repair authorisations.
Check if LW launches

If not throw it away and download the 5.2.2 beta version LimeWire 5.2.2 (Beta) - Lime Wire. This worked with me and I hope it does for you. If not please come back with more details. If you payed for a new Pro version, you probably still have the link to this page. If yes, you can find on this page the link to the 5.2.2 Pro beta