Try starting again.
Install Java first. You can either update to the latest version here (I have this one & LW's working fine): Java SE Downloads
or 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.

Next, download the LW offline installer. When you click to download & a dialog box pops up, cancel it. Now use the option to download the offline installer
Lime Wire » Download LimeWire


Since you're updating to 4.14.10, 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.