I'm building a custom TV Lift. I'm thinking of using a motor with
high torque that drives a basic block-tackle pulley system. Without
getting into electical engineering and power: I was thinking of using
either an old cordless drill, or corded drill.

I should think you'd have better luck using a threaded rod and
a big-ass nut. If you want to use cable, don't use a block
and tackle, use a windlass.