You need Java Runtime Enviroment for a lot of things. Not just Limewire. You need to reinstall it

Go to

http://www.java.com/en/download/manual.jsp

a lot of people recommend doing it manually, but you can choose an automatic install. just press the link from the page if you choose that option

Maybe it would be a good idea to try downloading Limewire too since the problem could be in the installer. Download the exe not the online installer