Use the offline installer, there's less chance of installation problems/corruption

Install Java first. Use the JRE offline installer here & remove your old Java version before you install the new one.
http://java.sun.com/javase/downloads/index.jsp

Now reinstall LW using the offline installer. It will automatically remove a previous version while installing the new one.
http://www.limewire.com/english/content/download.shtml