I'm pretty sure that, once a pixel on an LCD is set to a certain color, no more energy is needed to maintain that pixel until its color needs to be changed. That is, a black pixel requires just as much energy as a white pixel, but that the energy is consumed in changing each pixel to a new color and is only consumed during that update.
The real drain is the backlight, which is always shining and always blasting its way through every single pixel on the screen. That's why black isn't really "black" so much as it's "really really really dark grey".