Ordinarily 'high key' vs. 'low key' is not used to define the lighting of the scene, but it refers to the tonal balance observed in the final photograph. A photograph which has mostly dark tones, and very few light or white areas is 'low key'.
And you can shoot the low key photo with high intensity light or low intensity illumination...a mid-tone card placed in the scene would be rendered mid-tone regardless of the intensity of lighting, since you would adjust your exposure to suit the amount of light striking the scene. You can make a photo more 'low key', so that even the midtone card is rendered darker than its inherent brightness...but again, that has to do with Exposure, not lighting intensity.
It is possible to make things more 'low key' via placement of lighting...for example, a single Key (Main) light falling on the subject in such a way that little of the area visible to the lens is illuminated, and mostly the shadowed area is seen by the lens. The use of high contrast post processing settings would allow you to keep a bit of the photo 'white' but most of it would be lower in exposure and fall into the 'black' and 'dark grey', but this works far better with a subject that is inherently darker in tonal range, rather than a blonde bride in a white dress!