just 2 suggestions:
first of all you can use mesh - you just need to put AP on the roof of elevator car, and another inside of car, connected by cable. 100 - 130m is perfectly supported by mesh and works well, actually you can support even much longer runs using directional antenna.
But if you have cable available, use it as David advised. It is the best way. In recent projects we had fiber cable available to car (multi-mode, in newer single-mode is available too), so we used it for both WiFi and DAS connection, as well as for different data connections for screens, video, phone etc.