Jack is absolutely blind with rage and the fact his hands aren't instantly crushing her windpipe only fuels his resolve that this is, in fact, Lilith and he is going to kill her.

"You know what you did!" he snarls, shaking her now like a ketchup bottle that refuses to dispense. How dare she pretend not to remember ruining his life that day back in the vault? He was in a different form now, yes, but his hologram looked the same as his old body so that was really not an excuse. Not that he would have taken one from her anyway. All he wanted was to watch the life leave her eyes as he crushed it out of her.