I haven't found any way to kill her permanently.
I'm really annoyed by this one, I think I'm going to give up on my first honor mode run, because my goal was for this to be a critical moment for Lae'zel, killing Aylin. Apparently it's not possible. I rolled with the things I couldn't do so far, but this one just undermines too much of my planned arc. This sucks.
I'm disappointed by this turn of events. It feels stupid to me that other characters are not given a chance to kill Aylin, normally Larian doesn't railroad decisions like this.