Try updating to the latest version here (I have this one & LW's working fine): Java SE Downloads
or, if that one gives you any problems, try this older version, which has worked well for lots of people: Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11
Whichever Java version you use, download the JRE offline installer & remove any other Java versions before installing another one.

If that doesn't help, delete LW's preferences folder when LW's properly closed. See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will change all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.
In case you have Vista: LimeWire Pref Folder in Vista