What I am saying is that this uniform tension rubber-band system (UTRS or triangle method to most ppl) is misleading, this is because what we are trying to achieve is not uniform tension (or force), but rather uniform acceleration (as much as possible).
What all of us can agree is that the lift will definitely need more force when it is going up as compared to going down (with gravity acting on the lift as well). But what we are looking at is to get an as uniform resultant force as possible, so that the lift will always be accelerating at about the same rate at every point of its motion.
And what @callen (correct me if i am wrong) is saying is that we should play around with the triangle to get an uniform acceleration, rather than to aim for uniform force.