The Book of Mormon started out classifying the Lamanites as Lehi's decendants; mostly the brothers of Nephi. That is true enough. Something, however, happened that quickly made that identification muddled. Almost from the start the Lamanites consisted of at least two groups of unrelated peoples. There was Laman and Lemual and then sons of Ishmael. The Nephites had Sam and daughters (perhaps with some sons) of Ishmael. Soon, other groups start popping up everywhere. Some don't even seem to have a cursory relationship to Lehi. In fact, and this is what most Mormons miss and Hugh Nibley constantly pointed out, the primary ancestors of the Book of Mormon peoples were Jaredites! Nephites and Lamanites are meeting the Jaredites everywhere according to name patterns. I think the Mulekites might have been Nephites who ran into a large population of Jaredites and incorporated themselves into the political structure. Both the Mulekite Nephites and Jaredites lost their original cultural connections. The point is, there were other groups living and mingling with each other.
Along with the above diversified populations, there was an event that totally and completely destroyed the very concept of Lamanite and Nephite as family relationships. It was the coming of Jesus Christ. During his ministry both the Lamanites and Nephites, and all other peoples, became one community. It lasted at least a hundred years. After this short era of unity, Lamanite and Nephite became a religio-social designation.
4 Ne. 1: 20
20 And he kept it eighty and four years, and there was still peace in the land, save it were a small part of the people who had revolted from the church and taken upon them the name of Lamanites; therefore there began to be Lamanites again in the land.
It was a self-identy more than family lineage; although some sense of relationships might have inspired the usage. Even then, the designations became fragmented into other sub-groups. One of the most major writers/editors of the Book of Mormon seemed aware that his literally a Nephite was important enough to mention. There were plenty of other groups who weren't.
Mormon 1: 5-10
5 And I, Mormon, being a descendant of Nephi, (and my father’s name was Mormon) I remembered the things which Ammaron commanded me.
6 And it came to pass that I, being eleven years old, was carried by my father into the land southward, even to the land of Zarahemla.
7 The whole face of the land had become covered with buildings, and the people were as numerous almost, as it were the sand of the sea.
8 And it came to pass in this year there began to be a war between the Nephites, who consisted of the Nephites and the Jacobites and the Josephites and the Zoramites; and this war was between the Nephites, and the Lamanites and the Lemuelites and the Ishmaelites.
9 Now the Lamanites and the Lemuelites and the Ishmaelites were called Lamanites, and the two parties were Nephites and Lamanites.
10 And it came to pass that the war began to be among them in the borders of Zarahemla, by the waters of Sidon.
Criticism has been made that early and many modern LDS Church authorities have said that all Native Americans are Lamanites. It is claimed this make it official doctrine. The one place that should set the tone for official doctrine, the Doctrine and Covenants, is not as clear on the subject as first supposed. The Doctrine and Covenants follows the Book of Mormon in catagorizing and then qualifying the names.
D&C 3: 16-20
16 Nevertheless, my work shall go forth, for inasmuch as the knowledge of a Savior has come unto the world, through the testimony of the Jews, even so shall the knowledge of a Savior come unto my people—
17 And to the Nephites, and the Jacobites, and the Josephites, and the Zoramites, through the testimony of their fathers—
18 And this testimony shall come to the knowledge of the Lamanites, and the Lemuelites, and the Ishmaelites, who dwindled in unbelief because of the iniquity of their fathers, whom the Lord has suffered to destroy their brethren the Nephites, because of their iniquities and their abominations.
19 And for this very purpose are these plates preserved, which contain these records—that the promises of the Lord might be fulfilled, which he made to his people;
20 And that the Lamanites might come to the knowledge of their fathers, and that they might know the promises of the Lord, and that they may believe the gospel and rely upon the merits of Jesus Christ, and be glorified through faith in his name, and that through their repentance they might be saved. Amen.
Even in the Doctrine and Covenants there is a hint of a political, as much as lineal, meaning behind the names when it comes to teaching the gospel. A rejection of the gospel seems to be one of the ways to gain the designation "Lamanite" beyond who were your ancestors.
48 Yea, and this was their faith—that my gospel, which I gave unto them that they might preach in their days, might come unto their brethren the Lamanites, and also all that had become Lamanites because of their dissensions.
It would be nice to know what percent is "brotheren" and "dissenters" in the makeup. As it is, that could be anyone's guess. There is no doubt that the names Nephite and Lamanite still hold very specific family meaning. When you speak of Lamanite, it can very well be understood as having a relation to Lehi. However, the relationship is thin. It is more like saying Latter-day Saints are of the House of Israel. True enough from a spiritual standpoint. If we are to believe the Scriptures that is true from actual fact; as long as we understand the dilution of the original Israelite blood in our Gentile genes. So, from that perspective the Lamanites are the main progenators of Native Americans. Problem is, that isn't saying much. The original gene pool was mixed up, changed, scattered, and redefined long before Columbus. The answer to the DNA question is in the Book of Mormon. It just takes some paying attention.