Have you finished reading . . . . . . . . book I lent you?

The correct answer is D. no article.

The article "a" or "an" is used before a singular noun that refers to a general thing or person. In this case, the noun "book" is not referring to a general book, but to a specific book that the speaker has lent to the listener. Therefore, the article "a" or "an" is not necessary.

The article "the" is used before a singular noun that refers to a specific thing or person that has already been mentioned. In this case, the noun "book" has not been mentioned before, so the article "the" is also not necessary.

Therefore, the correct answer is D. no article.