In order to understand why a lung shot with a weapon of any sorts is looking for trouble on an elephant you need to understand the anatomy. I have conducted autopsies on elephant in Kruger, and their lungs, due to the weight, are attached to the inner thoracic wall.
This opposes the mechanism in any other mammal, where the lung is a loose organ, supported to the inner thoracic cage via a potential space and negative pressure. Correctly termed, this is where the visceral pleura sticks to the pariatal pleura via above mentioned negative pressure.
A penetrating chest wound of any sorts will allow the lung, or in the case of a double lung shot, both lungs, to collapse causing difficulty in breathing and more haemorrhaging into the lungs. This is known as a pneumothorax, and when filling up with blood a haemopneumothorx. The animal breaths faster and faster, speeding up the process, which leads to their rapid death.
In the case of a penetrating chest wound in an elephant, you simply have a hole in it’s lung, which might or might not have hit a blood vessel. That leaves the animal with a fairly benign hole in his chest, as well as two very functional lungs. He might take days to expire or recover. Think of all the elephants found with musket balls in their chests after being hunted years later.
Obviously a heart shot traversing the mediastinum and severing the large thoracic arteries will cause the sufficient haemorrhage to kill the elephant, but it is a difficult shot and takes deep penetration, coupled with the hope that the arrow or bolt does not deflect on its way there.