My network is besieged by attempts to enter on port 6346; the person who put Limewire on the LAN has taken it off, but the router logs still show the attempts from outside. The LAN and my business is largely down.

Two questions:

How long till the machines on the outside figure out not to bother ? How is the code on the client side written to this issue ?

Is this actionable ? Can I sue Limewire for what amounts to a D.O.S. attack ?

It shouldn't take long. Their shares are probably still caught up in the hash that people are finding. But then again, the other people may actually be related to this Organisations trying to connect via Port 6346. Blame such organisations!
(You must have a weak/sensitive connection for it to be affected like that.) BTW nobody "owns" the gnutella network! And there's many, many gnutella programs not only LimeWire. Those inquiring may have been using other gnutella programs.

You could try running Peerguardian to see if it is infact organisations that are portscanning

You can get it here:

http://phoenixlabs.org