I am not sure what to make of the film mentioned in this article. The film appears to be a bio-pic about C. S. Lewis and the article focuses on the apparently rather stormy relationship between Lewis and Tolkien. I am curious whether the relationship had been consistently stormy through its several decades or if it was just in the 50s. In that decade, Lewis wrote Narnia and married Joy Gresham. The latter apparently strained Lewis and Tolkien's relationship because Lewis neglected his friends in favor of his newly discovered love. I've read elsewhere that (can't remember where) that Tolkien resented the fact that prior to Lewis' marriage, Lewis was not sensitive to his friends' spending time with their spouses. Once married, he drastically changed his tune. That stuff happens, it just happened to these two later in life and probably when they less able to deal with it.
The former (Narnia) - well, I can well imagine Tolkien being bothered by it. I see LOTR as akin to a Victorian house or a Craftsman home - every detail thought through, every opportunity taken to be ornate. When Frodo and Sam are traversing the woods (I think in Ithilian - see note below) after leaving the Black Gate (in TT), Tolkien describes the forest in such wonderful detail. There is nothing like that in Narnia. Or when Gandalf cries out at the Khazad Dum (see note below), "I am a servant of the secret fire, wielder of the Flame of Arnor (see below), you shall not pass!" - this is evocative of the Holy Spirit and of tremendous spirituality in general, but it is not allegorical or even ostensibly Christian. Aslan dying or Diggory in the garden (in Mag. Nephew) is almost crass in comparison - what Lewis might have called "fairy tale" does come across as almost biblicist or Christian propaganda (Mary Bowman would delete the "almost"). Yet here is the thing. I don't think that one should compare LOTR and CofN. They really are different. LOTR is the essence of mythopoieia, (sub-)creation for the pure joy of it. I think all the children Lewis knew were the ones he dedicated his Narnia books to - but still he cared about children and he cared about them spiritually. Where Tolkien was creating for the joy of creating, Lewis had found another way to evangelize, to pastor, to preach - it was his calling and I doubt he could have resisted it. CofN do not have to be read as Christian to be enjoyed - but, nonetheless, one cannot read them as anything but preachy - Lewis is preaching about the evils of modern culture (its new educational systems, its twisted view of the environment, its limiting view of human nature and human imagination, etc.). He offers Narnia as a great "What if" - not just "What if Christ were a Lion in another world" [his arg. that Narnia is not allegory], but "What if children from our world were brought to live in the classical, pre-industrial, magical, and ultimately baptized world of faerie." How would they see life differently? So it's world building, even mythopoieia of a sort, but with the intention - in the narrative and in the sharing of the narrative - of bringing this world's children into that world. It is, as I said, essential evangelistic.
Note 1: I just got my kids in bed, I'm tired and I refuse to look up names in LOTR or to fact check. What's left of my memory is repsonsible for the above.
Note 2: Tolkien is open to criticism of being Narnian before Narnia in the way LOTR ends. The Scouring of the Shire (see n.1 above) is a wonderful section and I am glad he wrote it - but on one level it is as crass and as "preachy" as anything Lewis ever wrote. Aslan dying for Edmund and Sharky's industrial blight in the Shire - they are both as obvious as the day is long and, in spite of it, both remain as beautiful and wonderful to read.