In addition to books we know from the Bible, the plates of brass also contained specific genealogical records. Lehi learned that both he and Laban were descendants of Joseph. That tells us why Laban had this particular set of scriptures. He was appointed, or perhaps self-appointed, guardian of a lineage record. That lineage record included the sacred writings that others were also protecting, but it was specialized for that lineage.
It would be surprising had Lehi not known his tribal affiliation. The importance of that record on the plates of brass was to make it real, and definable. When Lehi’s family would arrive in a new world, it is likely that this relic of lineage authority became important in the Nephite community. This scene does bookend Nephi’s statement from before the journey to retrieve the plates in that there was a genealogy of his forefathers on them (1 Nephi 3:3).
More importantly for the current story, tying the family to Joseph also tied them to the Exodus. They would be paralleling their ancestor’s journey through a wilderness. Nephi uses this as another occasion to make a reference connecting his family’s journey and that of the children of Israel who were led to their promised land.