I recently had a discussion in which someone asserted that the Narnia Chronicles was an allegory. I conjecture that people say that because we have become convinced by the repeated warnings of so many Christian critics today that it is bad for any piece of literature, especially fantasy, to be explicitly Christian, which Narnia is. So, any time we detect explicit Christianity in a work, we either relegate it to the category of pious fiction or, to save it from being explicitly Christian, call it allegory. You have to have written at least 70 years ago (Brideshead) to get away with explicit Catholicism. Didn't Flannery O'Connor avoid any Catholicism in her arguably Catholic fiction? Further, calling fiction allegory, which devotees of Tolkien will put in the "bad" category, is usually an indication that we think the "Christianity" of the piece is still too explict, and therefore objectionable--too transparent.
I think to call Narnia "allegory" is to misunderstand it.
Allegory is writing in which characters either a) represent abstract concepts or b) represent another reality. The characters in an allegory are often stereotypical and without well developed, complex character. There is no imagined direct connection between the allegorical world and the real world in which we inhabit. Often allegory has to do with the personification of aspects of the interior life. Think of Hind’s Feet on High Places, for instance, which is strict and pure allegory. So, virtues, passions, etc. are personified. Lewis did write allegory—Pilgrim’s Regress. Tolkien didn't like allegory
Why is Narnia not allegory, if Aslan represents Christ? The answer is because Aslan doesn't represent Christ. The entirety of the Narnia series is fictional, including those parts of it that take place in our world—including therefore the relationship Christianity to the concrete events that are imagined to occur in our world. Lewis imagines multiple parallel universes that have connections, including to our universe in which the Christ story occurred and the Pevenses live. The “what if” of Lewis’s story is, “what if there were parallel universes? What if one of them has intelligent, speaking animals? How might the Triune God interact with them?” Since God is One, He would act similarly in the other universe as he did here. Hence, for instance, the Second Person of the Blessed Trinity would become an animal. This is not allegory, but rather what Tolkien called “applicability.” None of the characters represent abstract ideas or other realities. They are, in their complexity, persons who interact with each other and the world so imagined. What might a complex human person do in these circumstances? Or a complex beaver person? Or the Second Person of the Blessed Trinity?
If one thinks Narnia is allegory, one would also have to think the Space Trilogy is allegory. Rather, it is simply explicitly Christian, which is also what Narnia is. It is explicitly an imagined world with has direct and explicit connection to our Christian story ("eldilla" as our angels, “Sons of Adam and Daughters of Eve.”)
One might be able to argue that the Voyage of the Dawn Treader is allegory, I suppose, but I think rather it is more properly described as Platonic. Lewis imagines that the voyage east is the way the relationship between what we would call earth and heaven works. Similarly to our imagining that heaven is in the sky. Are all stories in which heaven is imagined in the sky allegories? The Littlest Angel, for instance?