Well in the states, many cities don't allow these equipment in the elevator shaft. I think the best solution is if the elevator company can run an Ethernet cable in the shaft (depending on length) and place an AP inside the car. I have seen APs mounted outside the elevator doors and depending on the door, your signal can be lost when the door closes. You also have to look at the roaming from switching access points, which can cause an unreliable solution.
Other options is running a DAS in the elevator shaft. Speak with the elevator company to see what suggestions they have.