My guess is the charge was not immediate and straight at him.
The dogs and the lion might have interacted. He might have had time to drop the shotgun and draw his pistol.
One poster at AmmoLand said he might have trained himself to drop anything and draw the pistol...
Perhaps it went like this:
See lion.
Drop shotgun, draw pistol.
Lion charges.
Shoot lion.
Two dogs involved, multiple scenarios possible.
Similar thoughts.
The shotgun could have been broken open or even unloaded.
Being an former LEO he defaulted to his training.