I have just deleted the incomplete directory again and re-installed Limewire, all is OK. I think I have figured out why Limewire repeatedly re-created the incomplete directory inside my shared directory.

This time around it uses
c:\docs\My Music
c:\docs\incomplete
i.e. Limewire creates the incomplete directory at he same level as the shared directory.

Originally I shared and downloaded to a subdirectory of my music files
c:\docs\My Music\ogg
LimeWire saw fit to choose
c:\docs\My Music\incomplete
As the temporary directory. When I changed the shared directory up a level, Limewire stuck with the same place for the temporary files and thus I got a problem. Even when I deleted the incomplete directory Limewire just stuck with it and recreated it again in the same place.

I think this is a bug.

Limewire should allow the user to specify where temporary files go or at least put the them in a directory intended for temporary files.