Now we have this helpful little article, which says:
Tolkien and author C.S. Lewis ... bonded over the horrors they witnessed as WWI veterans, as well as writers' block with their two masterpieces, The Lord of the Rings and The Chronicles of Narnia series. It was actually the Catholic Tolkien who convinced his agnostic friend to convert to Christianity, which obviously helped get the creative juices flowing in crafting Narnia, Aslan, etc.Most of this comes out of the commenter's imagination, not even that of the moviemakers.
Tolkien and Lewis didn't bond over war horrors, which - in keeping with a stoicism common among veterans of both world wars - they didn't much like to talk about explicitly. Lewis's main comment about his memory of combat is that it was so "cut off from the rest of my experience [that it] often seems to have happened to someone else." Instead, they bonded over their love of myth and fantasy. What Lewis exclaimed to a childhood friend after meeting Tolkien was that he was "the one man absolutely fitted, if fate had allowed, to be a third in our friendship in the old days, for he also grew up on W[illiam] Morris and George Macdonald."
Lewis never suffered from writers' block. Ever. If Tolkien developed a jealousy towards Lewis, that facility was likely to be a reason. And it was Lewis's facility at turning out finished, or at least passable, prose, in particular. Tolkien did get stuck at times. But writer's block was not his real problem. He turned out reams of pages. But he kept niggling at his works and rarely got anything finished. Lewis churned it out with hardly a second thought.
Lewis wasn't an agnostic. That word does come from the original article, and it's wrong. He was an atheist, or more accurately a hater of God. Tolkien did help him overcome it. But by the time he stepped in, Lewis had already become a deist, a non-specific believer. It was encounters with many other Christians among his friends, the men who shared his values and interests, that had pushed Lewis in that direction. What Tolkien helped Lewis do was accept Christianity in particular, and he did it through their shared love of myth, by arguing that Christ was the true myth, the story that moves you as any myth does, but which really happened. (You want to read Lewis's Surprised by Joy, which explains all of this.)
Obviously without Lewis's conversion he'd never have written his Christian myths about "Narnia, Aslan, etc." (a phrasing suggesting its author doesn't know much about Lewis's fiction except that there are things called Narnia and Aslan in it), but Tolkien did not thereby "help get the creative juices flowing," because Lewis didn't need that help. See above about facility.
The one thing the author gets sterling right is knowing that The Chronicles of Narnia is a series and The Lord of the Rings isn't.