While culture is learned and typically passes from parents to children, people can change cultures or assimilate into different cultures. Thus we have Americans who are culturally American, although they (or their ancestors) might have come from Africa, Europe, Asia, or many other parts of the world. Terms such as "African," "Asian," "Jew," "LDS," "Indian," and so forth are social constructs, not biological or genetic classifications.
Although some of the original Lamanite party would have had Lehite DNA, anyone who joined the Lamanites was called "Lamanite" by the Nephites. After Christ's visit to the New World, Book of Mormon peoples lived in harmony for many decades. During that time, there were "no Lamanites, nor any manner of -ites; but they were one, the children of Christ" (4 Nephi 1:17). Several decades later we read of a small revolt of people who had "taken upon them the name of Lamanites; therefore there began to be Lamanites again in the land" (v. 20).