Expression: "Rent a book"

[Tom]

Hi

Can we use the word "rent" with a book--I mean, when we pay for the use of a book from a private library?

Do you find this conversation correct and natural?

On returning the book to the private Public Library:

[Mister Micawber]

.
We don't normally pay for books borrowed, so the phrase sounds odd to me in any contecxt.
.
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Native English teacher at Mister Micawber's