Donna Hill mentions arguments that Joseph was influenced by View of the Hebrews.
Donna Hill, Joseph Smith: The First Mormon (Garden City, NY: Doubleday, 1977), 104
A more recent historian has suggested that Joseph took his theme from Ethan Smith, a Congregationalist minister from Vermont (no relation to the prophet's family so far as is known) whose View of the Hebrews, first published in 1823, proposed that the American Indians were descendants of the lost tribes of Israel. In 1842 Joseph Smith mentioned Ethan Smith's work in Times and Seasons in the context of a corroboration of The Book of Mormon, but there is no evidence that he had an earlier acquaintance with it. It may be, however, that Joseph was previously aware of the idea of the Jewish origin of the Indians, since there was a great deal of popular speculation on that subject well before his time.
Joseph himself described The Book of Mormon as "coming forth out of the treasure of the heart... bringing forth out of the heart, things new and old." His attitude toward it was manifested in what he told the Twelve Apostles, that "The Book of Mormon was the most correct of any book on earth, and the keystone of our religion, and a man would get nearer to God by abiding by its precepts than by any other book."