Did you install the Java properly using the JRE offline installer of the newest version prior to the installation of LW? You could get it here (version 1.5.0_8):
http://java.sun.com/j2se/1.5.0/download.jsp
But before installing this version, uninstall all othet Java versions and reboot after uninstalling and after the new installation before reinstalling LW.
If that doesn't solve your problem, try to use the LW offline installer for "Others" OS systems at the bottom of the list of downloads available at the official LW site:
http://www.limewire.com/ 