Why not extend the knob/lever of the lock; that will reduce your torque requirements (though increase the length of travel needed, of course). If you are worried about modifying the lock, find out what make/model it is, and contact the manufacturer for a replacement knob kit - modify -that- part, and install it in place of the lock on the door.
Another option would be to use something other than a servo (perhaps a larger gearmotor, and figure out your own feedback/positioning system)...