The number seven is significant in the Bible to signify perfection or wholeness, as explained by Corbin Volluz:
God rested and sanctified the seventh day after the Creation (Gen. 2:3). The Sabbatical year is every seventh year (Lev. 25:4). Jacob served Laban seven years for Leah, his first wife, whom he thought was Rachel, and then another seven years for Rachel (Gen. 29:18, 30). Joseph prophesied seven years of plenty followed by seven years of famine (Gen. 41:26–30). God commanded Moses to displace the seven nations of the land of Canaan (Deut. 7:1). The Israelites took Jericho by circling the walls seven times on the seventh day, the ark being led by seven priests bearing seven ram’s horns (Josh. 6:1–16). Elisha commanded Namaan to wash (or dip) himself seven times in the Jordan River to be cured of his leprosy (2Kgs. 5:10–14). In the New Testament, seven baskets of surplus food were taken up after Jesus’s miraculous multiplication of the loaves (Matt. 15:32–37); and the book of Revelation abounds with sevens, including seven churches (Rev. 1:4), seven golden candlesticks (1:12), seven stars (1:20), seven lamps of fire (4:5), seven seals (5:5), seven angels with seven trumpets (8:6), seven thunders (10:3), seven last plagues (15:1), and seven vials (17:1).– Corbin T. Volluz – A Study in Seven: Hebrew Numerology in the Book of Mormon
Volluz goes on to explain how some scriptural authors go to great lengths to compose textual structures that accord with the number seven even when the number is only artificial. Similarly in the Book of Mormon, the tribes of Lehi are split into seven tribes, mentioned on three separate occasions including Jacob 1:13:
Now the people which were not Lamanites were Nephites; nevertheless, they were called Nephites, Jacobites, Josephites, Zoramites, Lamanites, Lemuelites, and Ishmaelites.
Why is Sam not included in the seven tribes? 2 Nephi 4:11 explains (using chiasmus) that Sam’s seed will be numbered with Nephi’s. This leaves Lehi’s tribes forming a perfect seven. Volluz notes how this is similar to the 12 tribes of Israel as Levi is not mentioned when the tribe of Joseph is split into Ephraim and Manasseh.
In addition to the seven tribes of Lehi, the Book of Mormon seems to intentionally use seven (or multiples of seven) in other places such as:
How was Joseph Smith able to work with the number seven like this when dictating the Book of Mormon?