I first read the Chronicles of Narnia in college in the early 70s. I had an appreciation even early on that Lewis "tackles difficult theological questions" with skill, as I would have put it then, and indeed for decades after. I had only vague thoughts of anything more specific. But reading them again two years ago and thinking about them with special regard to theme this year in preparation* for my adult Sunday school class on forgiveness, I see some specificity that I earlier missed.
In The Silver Chair, Lewis refutes Freudianism specifically (the Green Lady), with side trips to supporting a high view of scripture ("remember The Signs," in Deuteronomic fashion) and even weaknesses in Spinoza and Hume. In The Magician's Nephew, Nietzsche on the lips of Uncle Andrew and Queen Jadis is refuted ("a high and lonely destiny" and higher versus lower moralities - I can't tell you how much this quote frightens me), the universality of Natural Law shows up in The Lion, the Witch and the Wardrobe (plus Plato in guest appearance), and syncretism is exposed in The Last Battle, along with, well every heresy in the history of Western Civ, frankly. Lewis was apolitical in the immediate sense throughout his life - he took no newspapers and did not want to be bothered. But legitimacy of rule is a theme in every one of the Chronicles. (It is prominent in Tolkien, an anarchic monarchist as well.) There's more, if you want to look at the other volumes. It's fun.
Lewis's first work of fiction was The Pilgrim's Regress, from which I learned a great deal of modern philosophical thought in condensed form. It has flaws and clumsiness, but it is perhaps the strongest echo of the Narnian Chronicles in his other work. And every work of Lewis is present in every other, it seems. The threads between each are numerous. He rewrote P's Regress, but for for children two decades later, in fairy story form. He is providing answers and armor for children against dangerous thinking long before they will encounter it directly, while they are only seeing the indirect effects in their schools, their media, and even (gulp) in their churches.
The over-obviousness of the Aslan/Christ resurrection symbolism in LWW bothers some adult readers, and I thought it was too much myself on first reading. But I was studying theater and literature at the time, with Christ-figures hidden behind every bush, as far out as Christopher Robin and King Lear, and was looking with jaded adult eyes already, so likely that's not fair. Yet as one follows this series that recedes, and one can see Aslan as God the Father or as the Holy Spirit in other volumes. The Trinity is underplayed and interwoven. Further, even in his own day Lewis noted that readers did not pick up the obvious Christian symbolism in his adult Sci-Fi Ransom trilogy, and that has certainly not improved in ours. An anecdote from one of the professors who teaches a CS Lewis course. At a Christian college even, a young woman told him she could tell that the scene at the Stone Table was important and it reminded her of something, but she couldn't put her finger on it. "But can't you think of someone else who dies but then comes back?" he asked. The light dawned. "Oh, right! Gandalf!" (I would give 30% credit for that answer on a test.) So overobvious to me, but mixed with the Norse, Greek and Roman, Celtic, and even Arabian mytholgical references, and geared to children, I long ago decided to withdraw my objection. The biblical themes are first among many, not exclusive.
These are not children's books. They are adult books written in a form children can access. Sometimes Fairy Stories... etc. They are an introductory course in unlabeled philosophy.
*My preparation seems to consist of reading stuff and thinking about it a lot, but not so much deciding on presentation. Probably not the best approach. Not a real teacher's approach.