iPad (Air) as 2nd screen using Lightning cable?

Bluetooth is not possible:

Bluetooth does not provide enough network bandwidth, or throughput, to be able to support Air Display.

If the device is jailbroken, you can tether the device to your computer over USB and use Air Display this way.

  1. Install Air Display on both OS X and iOS.
  2. Install MyWi and connect the device to OS X using USB.
  3. Turn on USB in MyWi.
  4. Select the device from Air Display's list of available devices.