So the situation is that there you are some place and then all of a sudden a person at distance identifies you as a potential victim and proclaims, "Bcwitt, I am going to hurt you!" and then runs at you?
Anything can be a deadly threat, though may not be recognized as such. In the last few years, we have seen quite a few people killed, brain damaged, or otherwise hospitalized in single punch attacks by apparently unarmed people that did not use a weapon, but just because a person threatened to punch you isn't likely going to go over very well (most of the time) if you retaliate as if it was somebody threatening you with a gun or knife and you shoot them.
Unless you can cite some other mitigating circumstances, an "attacker" not known to be armed who running toward you isn't apt to be considered a lethal threat unless indicated otherwise by action (e.g., trying to strangle you) or producing a weapon.