I suspect that your Java installation didn't install properly.
I'd reckon uninstalling LW and all Java versions on your computer, rebooring and then downloading the JRE offline installer of the newest Java (1.5.0_08) from here:
http://java.sun.com/j2se/1.5.0/download.jsp
Installing it, rebooting and then try to reinstall LW.
If that doesn't solve the issue, go and get a different installer exe from the official LW site:
http://www.limewire.com/
You may choose under OS "Others".....