I'm having the above problem in a new install of Lisa, and I'm baffled by it.
I'm starting it from the console, and it's showing the same messages I'd always expect from Conky, no error messages of any kind. It just never appears on the desktop.
I've tried changing the .conkyrc settings,specifically own_window_class setting, but it doesn't seem to make any difference at all. I've also tried changing the setting which has the file manager manage the desktop, no effect.
In MATE, on the other hand, conky works fine. I also installed Unity through the software centre and Conky doesn't show in that either.