In a homicide scenario, the angle to me sounds like he was on his back, on the ground, and the person was standing slightly "behind" him, looking down his body. I'm not sure if that makes sense. But imagine you were on your back, and someone was standing at your head, facing your feet. But probably back a slight distance. If the person with the gun simply shot too high for a head shot, it would be at about the right angle.
It may be possible that there was a struggle, the LT tried to use pepper spray, but they wound up on the ground with a struggle for the gun. The subject shot the LT in the vest during the struggle, at which point he was probably hurting pretty good and couldn't fight much anymore. The person gets up as backup arrives, shoots the LT because dead men don't make good witnesses, drops the gun, and bails before they find the body.