Do Airbus aircraft have an "off" position for their landing gear?
I was working for Airbus before, never seen it on A300, A320, A330, A340, A380, A350 or A400M. Only Gear Up or Gear Down position.

For confirmation on A320, here the FCOM section:


  NORMAL OPERATION
  The flight crew normally operates the landing gear by means of the lever on the center instrument panel. The LGCIUs control the sequencing of gear and doors electrically. One LGCIU controls one complete gear cycle, then switches over automatically to the other LGCIU at the completion of the retraction cycle. It also switches over in case of failure. The green hydraulic system actuates all gear and doors. When the aircraft is flying faster than 260 kt, a safety valve automatically cuts off hydraulic supply to the landing gear  system. Below 260 kt, the hydraulic supply remains cut off as long as the landing gear lever is up.