If there were any possibility of confusion over who this prophesied seer was, it is eliminated in verse 15, which declares that he would be named after Joseph of Egypt. Thus, the seer’s name would be Joseph, and his father’s name would be Joseph. This prophecy obviously identifies Joseph Smith as the seer, but it also has a subtle emphasis on the continuation of the importance of Joseph of Egypt. The connection to Joseph of Egypt is implied in the both the name, and the repeating of the name.
That emphasis is made clear in verse 16, which specifically notes that Jehovah promised Joseph of Egypt that his seed would be preserved forever. Without worrying about genetic inheritance, the names declare that Joseph Smith, Sr., and Joseph Smith, Jr., are symbolic continuations of the lineage of Joseph of Egypt. Lehi is declaring the future seer as the inheritor of the lineage of Joseph.