The rationale for exercising lung muscles makes some sense to me now given this information from Gaiam:
"There is a strong relationship between the strength of our breathing muscles and how breathless we feel. A useful analogy is to think about how much lighter a dumbbell might feel after you've trained your muscles for 12 weeks, compared to how it felt when you first lifted it; stronger muscles lessen the effort sensation of all muscle actions, including breathing."

This gives me a new appreciation for the deep breathing you do in yoga, which I imagine provides a similar benefit.

And here's something really interesting that I didn't know before I read about this device: women have smaller, weaker lungs than men:
"Not only do women have weaker inspiratory muscles than men, but research from the USA suggests that there may be another important factor which make strenuous exercise even more challenging for women - smaller lungs. Even when the smaller physical size of women is taken into account[ ], their lungs are still smaller than men's. Because of their smaller size, women also have narrower airways, which means its harder to move air in and out of the lungs."

So, as I choose to interpret it, this means that in terms of effort, 45 minutes on a treadmill for me is equivalent to . . . let's say at least an hour and a quarter for a man.