Back in the mid-1700s there was a fellow named Boturini who traveled through Central America gathering historical writings about the Aztecs and other native peoples. The Codex that bears his name depicts the story the Azteca/Mexica people told about where they came from and some of their history. Here is part of the first page:
First I'm going to quote the Wiki article on Codex Boturini, then I'm going to reread it the way it sounds to me.
The codex depicts the events of the Mexica migration from Aztlán and their history from the years 1168 to 1355 AD.[3] It begins with a priest leading Chimalma, fabled ancestor of the Azteca, from Aztlán via a boat.[18] Once they arrive at the shore, near Colhuacan, they build a sheltered altar for their god, Huitzilopochtli, who ordered this migration.[19] There they also encounter eight tribes that desire to accompany the Azteca.[20][d] The Azteca agree and the nine tribes set out under the leadership of the four god-bearers, Chimalma, Apanecatl, Cuauhcoatl, and Tezcacoatl, each carrying a tlaquimilolli.[21]
Over folios 3 and 4, the Azteca are transformed into the Mexica when Huitzilopochtli chooses them to be his people and teaches them to sacrifice blood to him. He also instigates the split of the Mexica from the other eight tribes ... . An Aztec (left) carries out Huitzilopochtli's instruction to break from the other eight tribes in a nighttime discussion. ...
What I hear:
It begins with a priest named Lehi, traveling from Jerusalem via a boat [1st Nephi 2-17]. Once they arrive at the shore, they build an altar for their god, Jehovah, who ordered this migration [1st Nephi 18]. They also encounter other people who accompany them, under the leadership of his four sons, Laman, Lemuel, Sam, and Nephi. The Lehites are transformed into Nephites when God chooses them to be his people and teaches them to sacrifice [animal] blood to him. He tells Nephi to split from the other tribes [before they kill him]. Nephi and the righteous flee in the nighttime [2nd Nephi 5].
For a mostly-oral tradition passed down over 1000 years until it's drawn up in the Codex, I find the parallels between the journeys more than coincidental. I found Boturini from reading Elder Moses Thatcher's pamphlet, Divine Origin of the Book of Mormon from the 1880s.
