I think we had a thread on this book a while back, but I don't know where it might be. I remember being somewhat skeptical myself, though I admit I haven't read the book. I don't know if Ward is contending that Lewis set out to write a series of seven books corresponding to the seven spheres and the seven virtues, or whether it just ended up that way. I think any contention that Lewis set out writing the Chronicles with a final agenda in mind is silly - Lewis stated clearly that he didn't have any ultimate goal of the books. In fact, he started out to write only one, and then thought he was drawing it to a close after three, and then some of the other ones surprised him.
If, however, Ward is contending that a correspondence rose up out of Lewis' classical education as he wrote the stories, that would be much more reasonable.