My recollection is that the transmission spectrum of most LCs are not even approximately neutral. Anyway, you might look up the Kent State liquid crystal institute. They do have a wall on a fab room at Kent that can be variably darkened, and I recall some discussion there long ago about making variable-tint windscreens for cars. Turns out to be rather expensive, I think.
At one time I investigated the use of the photochromic materials found in the 'transitions' sunglasses. That may be possible. And you'd not need a power supply