That a single English fantasy author could be staunchly xenophobic is perfectly feasible and you could bring your own substantive sources to the party if you want to deny it in this particular case.
I used cabal to highlight that C.S. Lewis is hardly unique -- if you think he's a xenophobe I can't imagine what you think of Tolkein or even modern authors like George R. R. Martin.
Knowing that, reading the various books it's hard not to believe that the Narnia Chronicles were written partly to promote Christianity, and the Middle-Earth works were written partly to explore fictional languages.
There's no doubting they were written in an overtly Christian context; does the author speak about using the allegory as a means of proselytising? Or, is that conjecture?
Absolutely not. The books are incredibly in your face, even kids recognize it.
> How does that promote Christianity, perhaps to 'reinforce it for those raised as Christians'?
It is not promote christianity as in telling kids to become christians or much about god. It promotes christian values - how you should behave what you should think about situations. You may read the books or go to sermon and they boil down to pretty much the same thing.
The first, second and third focus of every story is moral lesson you are supposed to take out of it. Any other purpose (story, fun, world building, suspension, whatever) is somewhere after. That is why the books are so popular among christians, imo. If you remove moral teaching, not all that much is left.
> Lewis's attempt at turning thinking, particularly child thinking, against the cultures found in the Middle East