Michael R. Ash summarizes LDS apologetic position on DNA and the Book of Mormon issue.
Michael R. Ash, "Lamanite Identity and the Book of Mormon," in Shaken Faith Syndrome: Strengthening One’s Testimony In the Face of Criticism and Doubt, 2nd ed. (Redding, CA: FairMormon, 2013), 195-207
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In summary, while there is no evidence for a genetic link between modern Native Americans and the Lehite/Lamanites (and there is no reason to suspect that Lehite DNA would be detectable in modern native peoples), LDS scriptures and prophets are justified in referring to them as “Lamanites” due to the likelihood of cultural and genealogical affiliations.