Would it be possible that a lack of calcium in diet cause bone pain?

Not likely : Unless you were severely depleted of calcium is is not really possible. Bone pain is common with certain forms of toxicity. Toxic accumulation of cadmium and other poisonous heavy metals in the bone can cause this type of pain. Itai itai disease is a form of cadmium poisoning where even light touching of the bones cause severe pain. It is associated with smoking and with industrial polution cars.