Verse 16 makes it clear that Lehi did not know which tribe he was from until he searched his genealogy in the plates of brass. It is not until Alma 10:3 that we learn that Lehi was a descendant of Manasseh, Joseph's son. Lehi's descent through Joseph is crucial to the "stick of Joseph" doctrine found in Ezekiel 37:16 and to the prophecies of Joseph who was sold into Egypt (Gen 29:22-26, see also JST Gen 50:24-38).
1 Nephi 5:14 If Lehi was a descendant of Manasseh, shouldn't he have lived in the northern "kingdom of Israel" which was sacked in 721 BC?
This is an excellent question. If Lehi's forefathers had lived with the rest of the tribe of Manasseh, in the northern kingdom, they would have been sacked by the Assyrians (see maps 5 & 9). They would have become part of the "lost ten tribes." Apparently, many of the "children" of Manasseh and Ephraim dwelt at Jerusalem with the members of the southern kingdom, composed of the tribes of Judah and Benjamin. 1 Chron 9:3 states, And in Jerusalem dwelt of the children of Judah, and of the children of Benjamin, and of the children of Ephraim, and Manasseh. (italics added) These individuals, whether of Benjamin, Ephraim, or Manasseh were all part of the Kingdom of Judah and therefore considered themselves Jews. Hence, Lehi was a Jew of the tribe of Manasseh.