The controller CAN operate at 72V but if you connect 36V battery, it should not have any problem operating at 36V.
I know of some BLDC controllers that can operate at wide range voltages but not sure what your controller specs are....
What is it exactly that you want to do? If you want to change your setup to a 72V 20amp rig to your motor, then you will need a battery that is rated for a nominal 72V, and the battery management system (BMS) that is built to allow a discharge of at least 20 amps continuous... So if you bought a new battery that is 72V10ah, it would have to be rated for at least 2c discharge (2c).
You probably should look at the throttle rating and any other displays you have attached to it.
Your 36v battery will only produce the voltage it was built for.... Serious rewiring inside the battery pack would be needed to get a 72v output.
IMO you would be better off selling what you have and go buy a monster rig like the MX3000