Yes, your existing battery should work fine with the Magic Pie, but you may need to reduce to maximum current setting on the Magic Pie's controller to prevent the battery from being overloaded.
Ideally, you need to find out the maximum continuous current rating for your battery.
Any of the Magic Pie range can be used as they are all multi voltage capable, you will just need to set the voltage of the controller to suit the 36V battery using the USB programming lead.
Alan