Search your computer for all files named "limewire" by going to Start>Search>Files and Folders. Delete all files you find.
Then open your registry by Start>Run and typing "regedit". There you go to "Edit>Find" and make also a search with the same query. Delete all keys of limewire.
Uninstall all Java versions on your system. Reboot and then download the JRE offline installer of the newest Java version from here:
http://java.sun.com/javase/downloads/index.jsp
Install it and reboot again, then reinstall LW using the offline installer.