So you installed JRE 1.5.0_11? Did you remove
all other Java versions from your computer?
Try deleting 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 it's still not opening, try changing compatibility (point 5 in the 'fixes' thread). If you're using XP, try compatibility mode for Windows 2000 or NT. If you're using Vista, try compatibility mode for XP.
Otherwise, reinstall LW & make sure to use the offline installer (when you click to download LW & a dialog box pops up, cancel that & you'll see an option to download the offline installer).