Try these fixes and see if they help...
Try uninstalling all versions of Java from the add/remove programs and then re-install the JRE 5.11 offline version....
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11
Right-click the Limewire icon and go to properties and change compatability setting to Windows 2000. (but only if you're using Windows 2000 or later.) Somebody reported changing to Windows NT compatibility fixed their problem despite not using that operating system version.
Right-click on the Limewire icon on the desktop and click on Run as. Then it should come up showing the current user and then switch it over to Administrator. (but 'only' if you're the admin of your comp.!)