In multiple places in the Book of Mormon, Lehi and his descendants (as well as Laban) claim to be of Joseph and Mannasah. Such as in 1 Nephi 5:14
And it came to pass that my father, Lehi, also found upon the plates of brass a genealogy of his fathers; wherefore he knew that he was a descendant of Joseph; yea, even that Joseph who was the son of Jacob, who was sold into Egypt, and who was preserved by the hand of the Lord, that he might preserve his father, Jacob, and all his household from perishing with famine.
If Joseph Smith was knowledgeable about the Bible, wouldn’t he know that the northern kingdom with Joseph’s tribes were scattered by the Assyrians?
Interestingly, recent research has shown that some of the tribes of Joseph were refugees in the southern kingdom, including those of high birth.
How would Joseph Smith have known this? If he wrote the Book of Mormon wouldn’t it be more likely that he would say Lehi and his family were from the southern kingdom?