No, nobody operates to GCI. I seem to remember that there have been rumours about Blue Islands looking into LCY-GCI, but I might be wring here.
As for ABZ-LCY, didn't Flybe operate to ABZ for a very short time in their British European period? I think City Star has been mentioned as the most likely operator for such a route. However, flights from ABZ to place like SVG and NWI are probably much more sought after than a service to LCY for which, I would guess, ABZ lacks sufficient demand.