Not strictly correct. The Lord of the Rings is a novel divided into three parts, each part being composed of two books. The division into six books was Tolkien's, although he did hope to see it published in a single volume. When Allen & Unwin suggested the work be divided into three parts, Tolkien paired up the books with uncharacteristically few complaints (see letter 136).

If you want, you can refer to each book as a part, in the generic sense of the word, but that is neither in accord with Tolkien's private thoughts or his published words.