Which version of Java are you using? Some people have had trouble with the latest Java updates. Try this version instead. Use the JRE offline installer & remove your current Java version before installing this one (it's easy enough to reinstall a later Java if it turns out that Java's the problem).
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

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 kill 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.
LimeWire Pref Folder in Vista

If that doesn't help, try reinstalling the latest version of LW (4.14.8) & make sure to use the offline installer (when you click to download LW & the download box pops up, cancel that & you'll see the option to use the offline installer).
Lime Wire » Download LimeWire

If all that fails, right click on the LW desktop icon > properties > compatibility & run in compatibility mode for Win 2000 or NT. If you're using Vista, run in compatibility mode for XP.