Count me in as another one who's having issues triggering Last Resort.
The problem seems to be that his approval isn't high enough, and his approval isn't high enough because after a certain point he just stopped gaining it. I've been following a couple online guides to try and nab approval from him, but when those instances come and go he never gains--or loses--approval whatsoever. I've also completely run out of dialogue options with him.
There's nothing I can presently think of that indicated I was locked out of anything...my Inquisitor was on good terms with him before he stopped gaining approval. Someone suggested that speaking to him about Alexius locks you out, but a friend of mine did that and had no issue with him in her playthrough. So it's looking like a particularly unfortunate bug to me.
I didn't concretely notice when he stopped gaining approval, but I think it must've been just after One Less Venatori, since I remember him gaining throughout that. Unfortunately I didn't think to make a separate save back then so I can't go back and test it.