JRR Tolkien believed that myth and symbolism kept much of meaning provided by the reader, while allegory was a demand by the author to read symbols in a particular way. For this reason he "cordially dislike[d] allegory in all its forms," and thought Lewis had strayed well into allegory in the Chronicles of Narnia. Tolkien also disliked any mixing of mythologies, believing that a work should retain a consistent background flavor. Thus, Lewis's dryads, centaurs, and Silenus struck him as at odds with the more Northern flavor provided by the dwarves and ettins.
On these points I agree, for I found several elements of the Narnia books jarring when I read them. Aslan remains Christic for much of the series, but in several places he is clearly Christ, and this pulls me out of Narnia, back into our world pretty rapidly. At the close of The Voyage Of The Dawn Treader, the adventurers are greeted on a shore by a lamb who is preparing them a fish. That's just too much. It's a nice idea, in a way - coming to the edge of one world we begin to see the obscurer symbols from another world, suggesting that in the borderlands Christ might take many shapes. Yet I find it heavy-handed.
On the other hand... I was stunned to learn that very few nonChristians pick up this symbol at all when they read it. Roman Catholics and fundies are heavily into this Lamb business, and the liturgical churches and the evangelicals likewise quickly pick up on Who is cooking on the shore. To us, talking lamb - way too obvious. Part of Lewis's aim in writing the series was to illustrate Christian theology in an attractive form to those who weren't familiar with it. It may not be fair of me to complain of a symbol being too obvious when it barely registers to its intended audience.
Similarly, Aslan as expression of the second person of the Trinity in a different world works pretty well for most of the series. In the first book, The Lion, The Witch, and The Wardrobe, however, he gets killed, breaking the tablets of the law, and comes alive again immediately after. That's just Jesus in a fur coat, not a myth or a symbol. And yet, a part of that symbolism that seemed overobvious to me - the breaking of the Stone Table which has the laws of the Emperor on them - has been missed by most others, even Christians. I have never seen or heard it commented on.
Lewis wanted to keep his theology tidy, I think, to prevent people from drawing wrong conclusions. Once the author has decided that death and resurrection are the key to redeeming any world - that the principle undergirding that act is universal - I admit it gets rather difficult for whoever the sacrificed god is to not look an awful lot like Jesus of Nazareth. Still, it has been done in part many times, not least by Tolkien, whose Gandalf descends into a hellish place to battle demonic monsters, perhaps dies, is reborn or recreated purified, and returns to save the land. This is not a definite Jesus - Tolkien has said that Gandalf, being one of the Valar, is an angel - but it is clearly derived from the Christ-story. It is less heavy-handed, among other reasons, because Gandalf does not return immediately.
Lewis defended himself by saying that the Narnian stories were not allegory, but supposals, an imagining of what Christ would look like and what he would do if he came into another world, with different intelligent fauna and a different history. We might wonder, perhaps, what Christ would do if he came and dwelt among Tolkien's elves. It is an imagining, a supposal, more common in science fiction than in fantasy. Lewis seems to have thought if Tolkien were more familiar with that genre that he would have been more understanding. This is possible, but I, for example, am more familiar with science fiction and I also found it a step too far, long before I had heard rumor of Tolkien's disapproval.
Tolkien also thought the entrance of Father Christmas was inappropriate, and I concur. When the Greek, Northern, and Christian mythologies are already fighting each other for space, the homely and specifically English Father Christmas is a step too far. Any of his incarnations, Santa, Sinter, Saint, would be too specific, an invasion of a single European nation's mythology into Narnia. The matter could have been handled much more indirectly, with winter gifts given by some less obvious figure.
These were errors, Tolkien believed, of a slapdash approach to writing fantasy. Lewis turned out the Narnia Chronicles one per year, usually in a single handwritten draft with emendations. Lewis wrote at most a second draft. Tolkien, who spent 17 years writing The Lord of the Rings, found this not merely puzzling, but abhorrent. From the retrospective view, most fantasy readers agree with Tollers rather than Jack Lewis: better to have a single jewel finely crafted, a mythology rich and deep and internally consistent.
Not so fast. Without Lewis's encouragement, LOTR would never have been completed, as Tolkien himself insisted many times. Left to his own devices, Tolkien would adjust mythologies and languages endlessly, unable to push things into final form. Even under pressure from his friend, the story very nearly never got written. The History of Middle-Earth eventually ran to 12 volumes, compiled by Tolkien's son decades after his death. Would anyone have bothered with the Silmarillion and Book of Lost Tales if the trilogy hadn't been completed? Tolkien's purist approach of infinite texturing would look less noble then.
As I have been noting lately, life is much more uncertain and unstable than we think. We cannot imagine a literary landscape without LOTR, but it nearly fell beneath the waves many times. The bulk of the manuscript was not read to the Inklings, as is popularly imagined. Hugo Dyson (or was it Havard? I forget) detested the book, and after a few sessions of muttering "oh no, not another f-ing elf," began to veto Tolkien's New Hobbit from being read Tuesday mornings at the Eagle and Child pub. Books two through six were largely read to Lewis alone, Monday evenings for over a decade. Without that, there would only be The Hobbit, perhaps Farmer Giles of Ham, and reams of disconnected stories, the eccentric hobby of an Oxford philologist, signifying nothing. The "slapdash" nature of Narnia would hardly come up then. Only by being spoiled by the depth of Tolkien's work do we notice the sketchiness of Lewis's.
There is also the small matter that they were trying to accomplish different literary goals, though they themselves barely apprehended this. I will bring that out when I discuss Lewis's influence on Tolkien (which some claim to be zero) in the near future.