The answer for those who can no longer open their LW 5.1 after updating their Java in recent days is to install the LW 5.1.4 version released to fix this problem
http://www.limewire.com/download/ or the LW 5.2 Beta which is quite stable:
LimeWire 5.2.2 (Beta) - Lime Wire
Pro users go to your personal Pro download page to download the recently released 5.1.4 Pro version. (Beta version link is on right side of page.)