Well, I certainly don't see a lunge. I know that gaps can be closed very quickly, even one like in the video, but, I don't see a lunge. From the looks of the video I think that you are right - it looks as though they fired in anticipation of a lunge, as a preventative measure. I don't think that amounts to a justifiable homicide.
Especially when the police themselves advanced to within the Tueller 21' circle.
Some years ago there was a video of a psychotic with a gun on a lawn chair on a sidewalk. Somehow those police didn't shoot the guy when they first approached. They held back and tried to talk him into getting help. Eventually, a sniper shot the revolver out of his hand.
i saw that video, awesome shot!