A correctly positioned mirror and reflective optocoupler will give one pulse per rotation of the pulley. If you use more mirrors you can get greater accuracy by producing more frequent pulses.
You need a reference point to tell you when the lift (elevator) is at a particular position, this might be at bottom or top of the shaft. Use this to zero your position counter then count the pulses that have been produced to calculate the new position.
There is a flaw in this logic which is easy to fix. With just pulses from the pulley it is impossible to work out which way it is rotating. The solution is to use a second mirror and sensor, positioned one half mirror width away from the first one. Obviously it will have to be nearer or further out from the axis so they don't overlap. Now you can tell which way it is rotating by seeing which sensor picks up the pulse first. You still need a reference point but now you can find the new position by either counting up or down at each pulley rotation.
For more information, look up how a wheel mouse works or look at quadrature encoders, they will explain the principle in more detail.
Brian.