A user on sourceforge kindly pointed out that Privoxy is for HTTP only, and that Limewire "will not work if you have either a web-only proxy or a SOCKS provxy" (quote from Limewire FAQ below):

See: http://www.limewire.com/english/content/faq.shtml#fir1

Apparently, Tor-Privoxy is really for anonymous browsing rather than becoming bogged down on P2P traffic.

So, for Limewire, another user recommends using: i2p, mute, or ants for anonymity.
(Source: http://www.dslreports.com/forum/news...full~days=2000)

The web sites for these anonymisers are:

i2p: http://www.i2p.net/
mute: http://mute-net.sourceforge.net/
ants: http://antsp2p.sourceforge.net/

Thanks again for your help LOTR.

Anyone please correct me if they have managed to get Limewire working with Privoxy-Tor!!

LimeWireMan.