C. S. Lewis is well-known for not calling himself a theologian. Rather than seeking a systematic theological perspective, he understood the story of Christ as a "true myth." As he explains:

It is true, not in the sense of being a 'description' of God (that no finite mind could take in) but in the sense of being the way in which God chooses to (or can) appear to our faculties. The 'doctrines' we get out of the true myth are of course less true: they are translations into our concepts and ideas.¹

Thus, it's not surprising that Lewis avoids taking a strong stance on a theory of atonement. In fact, he deliberately downplays the different theories in Mere Christianity:

We are told that Christ was killed for us, that His death has washed out our sins, and that by dying He disabled death itself. That is the formula. That is Christianity. That is what has to be believed. Any theories we build up as to how Christ’s death did this are, in my view, quite secondary: mere plans or diagrams to be left alone if they do not help us, and, even if they do help us, not to be confused with the thing itself.²

In the same chapter, he writes regarding a specific image of the atonement: "if it does not help you, drop it." He later clarified that he did not mean "reject" but rather that it "'need not be used' – a very different thing."³ Taking a position on this question is not necessary, he writes:

A man can eat his dinner without understanding exactly how food nourishes him. A man can accept what Christ has done without knowing how it works.²

Did he express a preference?

Though he takes this general approach, can we glean from Lewis's writings to see which models he preferred, or at least, ones he did not prefer? Yes, but the task is difficult. For example, the language of The Lion, the Witch, and the Wardrobe is actually less clear than an initial reading indicates: later in the book, the atonement is simply attributed to "deep magic" with no further explanation. Similarly, in Till We Have Faces, the mechanism behind a substitute sacrifice is not explained.

First, we can safely say that Lewis was not particularly comfortable with the penal brand of substitutionary atonement. In the aforementioned chapter in Mere Christianity he writes that "this theory does not seem to me quite so immoral and so silly as it used to"²—hardly a ringing endors*m*nt.

That said, he is more comfortable with a "fiscal" substitutionary atonement. He writes, “If you think of it as a debt, there is plenty of point in a person who has some assets paying it on behalf of someone who has not.” He continues, however, to further develop his idea of substitutionary atonement. It incorporates some of the language of subjective models of atonement, in that one purpose of Christ's death is to make it possible for us to surrender to God. By dying, Lewis says, the God-man undergoes surrender and death, making it possible for him to instill those characteristics in us and enable us to surrender to God and die to self.²

Elsewhere, in Reflections on the Psalms, Lewis again employs language reminiscent of a fiscal substitutionary atonement:

The price of salvation is one that only the Son of God could pay; as the hymn says, there was no other "good enough to pay the price." [...] As Dr. Moffatt translates [Psalm 49]: "None can buy himself off. Not one can purchase for a price from God (soul's ransom is too dear) life that shall never end."⁴

Substitutionary atonement is also clearly seen in Miracles:

He tasted death on behalf of all others. He is the representative 'Die-er' of the universe: and for that very reason the Resurrection and the Life. [...] Because Vicariousness is the very idiom of the reality He has created, His death can become ours.⁵

However, elsewhere he uses language more closely aligned with other models, such as the ransom to Satan model. In Perelandra, the divine voice says to the protagonist (named Ransom), "My name also is Ransom":

It was some time before the purport of this saying dawned upon him. He whom the other worlds call Maleldil, was the world's ransom, his own ransom, well he knew. [...] So that was the real issue.⁶

Views of scholars and theologians

Given what we have seen so far, it's not surprising that there is ongoing debate over which position Lewis held. Some evangelicals, like Kevin DeYoung, while valuing much of Lewis's writing, reject his understanding of the atonement:

I would argue his view is more like Christus victor or ransom to Satan than penal substitution.⁷

Others do the same but find a different view in his writing:

For Lewis the atonement is not fundamentally a matter of pardon, imputation and forgiveness, but rather the actual transformation of fallen beings into Christlike creatures. [...] Salvation is not primarily a matter of having our sins wiped away but rather overcoming the chief sin of self-will or pride.⁸

Ironically, disagreement is perhaps most heated with respect to the model displayed in The Lion, the Witch, and the Wardrobe:

The cover story of Time on April 12, 2004, asked, “Why Did Jesus Die?” and went on to present the three major theories of Atonement. The writers cited Lewis as a contemporary example for the “role model” or Subjective theory: “C. S. Lewis, the Christian thinker and author of the Narnia series . . . was not a doctrinaire exemplarist, but the lion Aslan, who stood in for Christ, was clearly a figure to be emulated.” Peter J. Schakel, responding to this assertion, argues, “The writers of the article definitely miss the point. . . . Aslan gives himself to the Witch as a sacrifice to make amends for Edmund’s disobedience. By focusing on that theory, Lewis takes a stronger [Substitutionary] stand than he does in Mere Christianity.”

Likewise, in reference to Aslan’s death, theologian Howard Worsely readily states, “The precise interpretation of the atonement is penal substitution.” Another Lewis pundit, Shanna Caughey, chimes in: “This form of soteriology is called substitutional atonement.” Meanwhile, authors like Charles Taliaferro (gleefully) and Matthew Hall (gloomily) state that Narnian Atonement theology lands most definitely in the Ransom, or Christus Victor, camp.⁹

Summary

The Lion, the Witch, and the Wardrobe can indeed be seen as a microcosm of Lewis's thought on the atonement: in it, Lewis refuses "to be bound by any one depiction of the Atonement."⁹ His other writing makes it clear that he does not see any need to settle on a particular theory of the atonement, considering it to be something beyond human understanding.

References:

1. Letter to Arthur Greeves, quoted in James W. Menzies, True Myth, 192
2. Mere Christianity, Book 2, Chapter 4, "The Perfect Penitent." See also The Problem of Pain, chapter 5.
3. Letter to Dom Bede, quoted in Walter Hooper, C. S. Lewis, 307
4. Reflections on the Psalms, Chapter 4
5. Miracles, Chapter 14
6. Perelandra, Chapter 11
7. DeYoung, "Cautions for Mere Christianity" (also archived via WebCite)
8. Scott R. Burson and Jerry L. Walls, C. S. Lewis & Francis Schaeffer, "The Nature of Salvation"
9. Touchstone, April 2009, "Mere Atonement" (also archived via WebCite)