I'm applying distortion control in-camera with Nikon's Auto Distortion Control menu option. If I apply profile corrections in Lightroom, am I double applying distortion corrections - Nikon's and LR's on top of each other?
Refer to the link below for info on the Lens profile support in Lightroom and Adobe Camera Raw.
See the reference to "cameras with built in lens profile support" if Lightroom is applying a lens profile supplied by the manufacturer of your camera you will see a indication in Lightroom other wise you will need to check and see if Adobe has a specific profile for your camera and lens being used. If you do not see that specific message then Lightroom is not using the setting you have made in the camera.
If shooting RAW (NEF) the camera does not apply any correction to the image data. The in-camera distortion correction only applies to shooting JPG.
Most lens profiles in LR are available only for RAW images and are not shown if you shoot JPG.
And to answer your question: In a normal workflow, it is not possible to double-applying the lens correction.