[small farm girl]

Actually, it was Chesterton that swayed him:
G.K. Chesterton had a significant influence on Lewis. As Lewis read The Everlasting Man, he appreciated Chesterton's humor and was surprised by the power of his presentation. He began to feel that "Christianity was very sensible 'apart from its Christianity'"
I'm reading Chesterton now, ...tough going.

[YogicCowboy]

Both are true: knowing Tolkien, reading Chesterton.

Tolkien and Lewis shared a passion for Nordic myth before Lewis converted.

Lewis dedicated The Screwtape Letters to JRRT.

[YogicCowboy]

Furthermore:

Lewis states in his memoirs that he was exposed to bigotry against Catholics. Tolkien and Chesterton were both Catholic. I strongly suspect part of the reason he immersed himself in the writings of Chesterton was because he already personally knew Tolkien.

Regardless, his autobiography, Surprised by Joy, recounts the effect of Tolkien’s witness upon him.

The Gospel Coalition references it thus:

“On September 28, 1931—just nine days after Lewis’s conversation with Tolkien on Christ being the true myth—Lewis took the final step in embracing the divinity of Christ while riding in his older brother’s motorcycle sidecar on the way to the newly opened Whipsnade Park Zoo in Bedfordshire. He recounts:...”

https://www.thegospelcoalition.org/blogs/evangelical-history/85-years-ago-today-j-r-r-tolkien-convinces-c-s-lewis-that-christ-is-the-true-myth/