I would suggest using a worm gear setup or a pulley system, With the pulley system providing the setup is clean and well measured it should easily drop using the weight of the LCD. Using stepper motors and a stepper control will allow you to have proper control over the lifting system.
There are a few options in which you can use this, I guess most would depend on how much room you have beside,front,below and behind the using itself.
I would personally use a scissor lifter which would be a single motor lifting the LCD from below with a contracting scissor that will expand/close the two rodes with a swivel mounted top plate. But having something flush and molded would be nice a clean..
Are you open to other options?