Just finished this mission. I wasn't planning on dealing with targets non-lethally when I started, because it can be tedious, but like many other games with optional stealth/pacifism routes, Dishonored punishes the player for not doing this. You get two runes for not wasting this chick, one from Pendleton and another from one of her sisters. Of course you don't really need as many runes if you're not going to be killing people. So maybe the canonical way to play the game is to spare the elite villains but murder all the guys just doing their jobs.