Do you use the Resume function on many files by the way. Do a search on the forum for Resume & eventually you'll get the idea.
May I suggest you try 2 things, one by one:
Delete LW's Preferences called
.limewire & found here: /Users/your_username/Library/Preferences/LimeWire (note: you'll need to reset our options so it might be wise to make a note of all your settings.)
Re-install Java using only the
Standalone Java installer
After installing any softw in OSSX you should repair permissions:
SAFE start & repair permissions