If someone is charging at me, I would take two preparatory actions before engaging:
I would try to move rearwards or laterally to create distance. Meticulously move away from the threat (not running backwards wildly). You will never outpace a maddened sprint towards you (he will eventually catch up) but the point is to give you a few precious additional seconds to analyze the situation and do what you need to do. Recall that on average, the findings of the Teuller Drill saw that, with no obstacles, a human being can cover (from a dead start) around 21 feet in 1.5 seconds. Even a half second of extra time is 7 feet. A quarter of a second is the difference between safety and two paws squeezing your throat. Staying stationary in a dynamic world is probably the worst thing you can do.
I would make all attempts to escape or evade, if safe to do so. This gives you more credibility as an individual that exhausted all attempts to get away from the situation thrust upon you, not an individual that escalated the situation. While in many states you can stand your ground, using obstacles and making attempts to create distance is probably more tactically sound, and friendlier in the courts.
Meanwhile it's probably wise to make very clear, concise, short commanding statements like "STOP RIGHT THERE" or "DON'T COME ANY FURTHER". If a weapon is present, "PUT DOWN THE WEAPON, DO IT NOW".
I feel this plays a multi-part role. A commanding presence can sometimes phase or stop an advancing individual since it is not a typically expected response from a "meek victim". Bad guys don't usually go for the biggest, strongest, most confident individual. They go for whom they think will make "easy pickin's" By flying in the face of stereotypical victim conventions, you might throw them off their game and make them reconsider. Asserting yourself might give the edge you need in a dire situation such as this. It might even help mentally prepare you, strengthen your resolve.
Second, it gives clear indication you attempted to diffuse the situation to any possible witnesses in the area, which will help your case greatly if lethal force is applied. Witnesses stating you attempted to escape and made statements to cease the attack establishes that you are the victim, NOT the suspect. Keep in mind that if lethal force is applied, law enforcement arriving on the scene see a dead or dying person, and you, an armed individual. The first thing they think of you is "suspect" unless exculpatory evidence stacks up and the picture is made clear that you were a victim that applied successful self-defense.
Given the guy's history and actions in this scenario I believe the shooter would easily be "No Billed" by a Texas Grand Jury (good shoot).
Assuming the viewpoint that you do not recognize or know the individual at all, either in person or by reputation, it does you no good in court. Just because you shot someone unknown to you and it happened to be an escaped serial murderer, you can't say, "but look! I killed a crazy axe-murdering cannibal!" Even if that bit of beneficial coincidence fell in your lap, it is not admissible as evidence in a court of law.
The valid counterargument is "but look! it could have been the pastor from the church down the street" Since you did not know the history of the individual, it played absolutely no role in your decision making.
