Try these things:
1. Uninstall Java using the Add/remove control panel. Then reinstall using the "Offline" Java installer.
2. Delete your LW preferences folder. See instructions for this & links to Java here:
Fixes for Limewire
3. Uninstall LW. Download & install the "Offline" LW version.
* If it still doesn't work, install Java 1.5 offline. But again, delete your LW prefs folder if there is any before opening LW again.