So I watched the video. It was in some ways frustrating for me, because I think Dawkins was continually missing the force of what Lennox was trying to say, but I also don't feel like Lennox expressed himself particularly well. I'm afraid he might have come off as presenting a god-of-the-gaps argument throughout. Every time he kept referring to the origin of something, be it the laws of physics or of life itself or of consciousness or the whole universe or morality or what have you, he came across as suggesting that science can't answer those questions, so we need to plug in God. In some ways, I think that
is his argument, but it is, of course, much more sophisticated. He distinguishes between good and bad gaps and later in the debate takes the typical DA view in which he thinks that God intervened at specific points in the history of the universe. That all lends itself to a god-of-the-gaps interpretation. But his more subtle point, and I think the stronger one that Dawkins completely missed, was the distinction in agency v mechanism. Dawkins wants to explain away the agent by explaining the mechanism. He went so far as to say that if the mechanism doesn't need an agent then you shouldn't posit one. But this is where Lennox had him dead to rights and let the whole thing go. You can have a mechanism that doesn't need an agent to operate it. That's perfectly fine. That's just a fully scientific understanding of the agent. But
just because the agent isn't a part of the mechanism, it doesn't follow that no agent is necessary. That's even true if you don't need to posit the agent to account for the
historical origin of the mechanism. Lennox' point was that the mechanism itself--its very existence, its very
nature--is suggestive of an agent. And it is that point: the intrinsic orderliness and intelligibility not only of the universe but of the physical and biological mechanisms by which it operates and develops, those mechanisms themselves are orderly and intelligible, and
that points necessary and unavoidably to the agent. And in light of that, Dawkins was allowed to get away with the basic question: how do you explain intelligibility and orderliness itself? Because however you explain it, you are just going to appeal to a mechanism
that is itself intelligible and orderly. The only way to explain it is to assume it, and to assume it is embodied necessarily in the only thing naturally suited to intelligibility and orderliness: Mind. So we come inescapably to a mind under and behind all of creation, such that all the mechanisms of science, far from burying God, simply illustrate His mind!
And that gets to the question of the OP. Dawkins is right insofar as simplicity precedes complexity. But Mind is simpler than physical and biological complexity. And when you really press things, you discover (in my opinion) that the Mind behind all of this is a Simple mind anyway, which is to say, you affirm the doctrine of Divine Simplicity. So says I, anyway.
fakeedit: I've often linked to a paper "Dawkins’s Gabmit, Hume’s Aroma, and God’s Simplicity,” which was published in Philosophia Christi 11 (2009): 113-27. I'll do so again
here as it explains in some detail where Dawkins argument regarding simplicity and complexity fails (as well as where it succeeds).