What to do if I was robbed in a poorly lit hotel parking lot, and suffered injuries as a result?

You may or may not have a claim against the hotel.

First, it's possible that the hotel may bear some liability for not lighting the parking lot well enough as a security measure, but that depends on the facts--how well lit was it? What is the area like? Where there previous thefts or assaults in the lot to put the hotel on notice of the risks? Etc. However, even if you can show they were at fault  for not lighting the lot better, your injury did not come from the robbery--you were injured when you fell in the lobby.

So, second, you'd have to show that either a substantial risk tripping when running away from the gunman  was a natural and predictable result of the robbery--because if it wasn't, then any fault for the robbery has no bearing on your injury; the robbery did not cause the harm--and/or that you fell due to some other unsafe condition that the hotel caused, like having a spill in the lobby it did not wipe up, or a loose step, border, or floor board that you tripped on, or a unsecured rug or torn carpeting that caused you to fall, etc.

So the fact that you were injured at the hotel does not itself make the hotel liable. You need to link, in a cause and effect manner, the injury to something the hotel did wrong.