Phil Ryken, president of Wheaton College, makes that argument in this essay:

Philip Graham Ryken. “Lewis as the Patron Saint of American Evangelicalism.” Pages 174–85 in C. S. Lewis and the Church: Essays in Honour of Walter Hooper. Edited by Judith Wolfe and Brendan N. Wolfe. London: T&T Clark, 2011.

Ryken first presented this talk to the Oxford University C. S. Lewis Society in 1995. The essay also appears in Beyond Aslan (2006), which you can read online via Google Books (pp. 69–81).

Ryken opens by quoting A. N. Wilson:

‘At Wheaton College in Illinois,’ he said, ‘where they are rather stupid fundamentalists, they have made C. S. Lewis into a god. They think he gives intellectual support for all their prejudices.’ (p. 174)

Ryken gives several reasons that Lewis is so popular among American evangelicals:

1. Britishness. “Lewis evokes for Americans all the sophistication and quaintness of England” (p. 175). His “peerless academic credentials” help give evangelicals “a sense of intellectual credibility” (p. 176).
2. Love of allegory. “Apart from the hymn, the literary genre within which evangelicals feel most readily at home is allegory. . . . [But Lewis’] narratives are mythical rather than allegorical. They evoke rather than articulate Christian doctrine” (p. 176).
3. Conversion. “Lewis’ own experience of conversion from atheism to orthodoxy is more than sufficient to establish his evangelical bona fides,” and his apologetic approach is distinct: “much of his apologetic work has an off-hand style about it, as if to say: ‘Look here, Christianity seems ever so reasonable to me, and here’s why, but you can take it or leave it.’ His apologetic method sometimes lacks the ‘You must be born again’ asseveration of Jesus in the Gospels, or the evangelist in the pulpit” (p. 178).
4. Fellowship with God. “To the fullest measure, Lucy [in the Narnia novels] had the kind of relationship with Aslan that evangelicals envisage when they speak of having a personal relationship with Jesus Christ” (p. 179).
5. Broad appeal. “More than anything else, it is Lewis’ children’s literature that has secured his prominence in America. . . . C. S. Lewis is the patron saint of American evangelicalism because he is fun for the whole family” (p. 180).
6. Ubiquitous quotes. “Sometimes it seems as if one can scarcely read a magazine or listen to a sermon without hearing a quotation from C. S. Lewis” (p. 182).

Yet “Lewis’ brand of Christianity seems incompatible with mainstream American evangelicalism” in some ways:

1. Inerrancy. “Though strong on the historicity of the gospels, Lewis is weak on the inerrancy of Scripture . . .” (p. 177).
2. Christian liberty. “Walter Hooper has long enjoyed recounting the story of the visit Lewis was paid by the well-known American fundamentalist Bob Jones. Upon returning to the States, Jones is reported to have said, ‘Well, he drinks, and smokes, but I think that man’s a Christian!’ Americans such as Bob Jones have been willing to overlook what they perceive as Lewis’ flaws—even to learn from some of them—because they are counterbalanced by a cluster of theological distinctives that lie at the heart of evangelical theology” (p. 178).

Ryken recounts how deeply Lewis has been a part of his family, including his grandparents, parents, and children. One of those stories is about a wardrobe:

Much more impressive than Lewis’ juvenilia [i.e., relics that Lewis wrote as a child that are part of the Lewis artefacts kept by Wheaton College] was the richly carved and ornamented wardrobe which then guarded the entrance to the English Department. It was, of course, the wardrobe, the one that had belonged to Lewis’ grandfather and had been shipped from Belfast for reassembly. Westmont College in California had rescued a second wardrobe from the Kilns, Lewis’ home near Oxford, but at Wheaton we always regarded the Westmont wardrobe as an imposter (although, to be fair, some insist that the Westmont wardrobe more closely matches the description in The Lion, the Witch and the Wardrobe). That Lewis’ personal effects can arouse such an argument demonstrates that he has become the patron saint of American evangelicalism, for few things convey legitimacy upon a potential saint as effectively as disputed relics.

Although the wardrobe at Wheaton was always kept closed (for safety?), I could hardly walk by without experiencing a frisson of anxiety. Did my father ever step inside for Narnian adventures? After all, who would ever know, since Narnian time does not consume any earth time? Or perhaps recalcitrant college students were muscled into the wardrobe for a dose of the Eustace treatment. Given such imaginative stimuli, it was little wonder that C. S. Lewis almost seemed like a family member. (p. 181)

I opened and peered into that wardrobe earlier this year when visiting Wheaton’s campus again, and I know the feeling.