You bring up a good point with your comment of "If the good guy chaser wasn't authorized to use lethal force in this instance - it may well be self-defense on the crook's part to draw a gun."
I seem to remember years back one of the required videos for the NC concealed carry class showed a scene which was similar.
If the criminal was retreating, leaving the area, it could be difficult to prove self defense, since the good guy was chasing after the criminal at this point, so, technically, the tables were turned.
To the OP,
I would not say its wrong or illegal to help your neighbors, or to defend them, even with lethal force if needed. We all should be careful because as I said in my reply to Glenn, it can be difficult to argue self defense if the criminal is retreating, or leaving.
Perhaps a good course of action would be once the criminal had left, to take the neighbor/friend, etc in to your house/car/what have you and call 911 for help, and be a good witness, while rendering any basic medical help if needed.
Just my opinion. feel free to disagree and enjoy the day!