Take a look at the world around. Single parent homes are "normal." Cruising cyberporn is "normal." Gay marriage is "normal."
I think Lewis was evoking Matthew 22:14. In a world corrupted by sin, "normal," simply doesn't make the cut. We are called to rise above, "normal," and the tedium of our daily lives.
Years ago, as a teen, I attended a presentation in which the presenter drew an X-Y graph. "Normal" behavior was all the way to the right, "Abnormal," all the way to the left. "Healthy," was all the way to the top, "Unhealthy," all the way at the bottom.
For example, relatively few people engage in rigorous daily physical workouts, although that's a very healthy behavior, so that would be plotted quite far to the left, but up toward the top. Eating garbage fast food for every meal, every day would not be considered, "normal," and would certainly be, "unhealthy," and plotted in the lower left.
This presentation has informed much of my life in the ensuing decades, and it applies not just to physical health, but also fiscal practices, and spiritual and moral behaviors, etc. The more I've reflected upon and plotted my behaviors, the more I've come to recognize that things considered, "normal," and things considered, "healthy" are often at great variance.
Fascinating concept, I’d like to subscribe to your TED talk.
(Not really being sarcastic - that sounds like a very interesting thought experiment. I’ll have to look at it more closely later.)