If you uninstall it correctly. Use Start menu -> Programs -> LW -> Uninstall. Then search entire computer to remove any trace. See http://www.gnutellaforums.com/291318-post22.html But still no guarantees. I'd actually recommend creating a test account, & try running LW from there. Of course your firewall will need to be checked to allow LW access.

When installing Java, always choose the "OFFLINE" JRE version to download to your computer. Then install it. Don't use the online installer because that's where lots of problems occur. Same principle applies to LW.

The version of Java recommended for you to try was Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11
Also see Fixes for Limewire (click on blue link) & check the options there.