Try these tips (using the offline installers)...
Uninstall your 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
Then uninstall Limewire using the uninstaller which is found in start > all programs > limewire...then re-install it using the offline installer...To find the offline installer, use the link below > cancel the installer window when it pop's up and then select the offline installer link...
Lime Wire » Download LimeWire
If those fixes don't work try deleting your preference folder...
Fixes for Limewire when LW isn't operating as it should