CS Lewis did write allegory on occasion - notably in his book The Pligrims Regress. But the Narnia books were not in any real sense allegorical, but rather analogical, or in a word used in this context by Tolkien, "applicable".

I mean, the narrative has parallels with other stories and with the real world, but it stands on its own. That's a very common aspect of much fiction. But you can't go through it saying this stands for that and that stands for this and so on, in the way you can with a real allegory, such as Pilgrim's Progress, or Lewis's reworking of that.