Here is an idea.
Place a RF, IR, or superbright Led on the lift box. At the top of the lift shaft put a sensing transducer. Because the intensity of the recieved signal will very as the range you should be able to experimentally determine the sensing circuit parameters for the proper position at each floor.
Because dust, humidity, and other factors will affect the attenuation of your transmitter; it would seem some type of RF device would be best suited.
To "Call" the lift: The position signal can be compared to the target reference. That reference could then be used control motor direction.
There are auto manufacturing companies putting small radar units on high end models. Researching those systems might give you some ideas.
Gavilan