Exactly. The lag isn't due to the autofocus. There is still a lag when snapping the pic even after holding the button down halfway to focus. It annoys me, as well. I don't know any way to fix it. There hasn't been an OS update in quite some time so it may not get fixed.
My experience is that photos take more than one second if not holding the button down half-way first but much less than one second if holding the button down half-way and letting it auto-focus in advance. I'm running .250. Of course, YMMV.