One of the questions that arises early for readers of the Book of Mormon is how Lehi, who is not a Levite and certainly not a descendant of Aaron, can offer sacrifice (1 Ne. 2:7), a privilege which, in the Torah as we have it, is restricted to those lineages.
The simplest answer is that this whole concept of an Aaronic or Levitical priesthood did not exist in Lehi's time.
The name Aaron occurs 50 times in the Book of Mormon, as the name of several different people and places. Not a single one of these occurrences refers to the biblical Aaron, brother of Moses and father of the priestly lineages. There is a vague reference to "a Moses" -- perhaps Moses himself, perhaps some later person figuratively so called -- having "a spokesman" (2 Ne. 3:17), but that's as close as we get to the Aaron of our Old Testament. There is no indication that this spokesman is Moses's brother, that his name is Aaron, or that he is a priest.
The name Levi occurs five times, four of which refer to a Jaredite of that name. The other does refer to the biblical Levi, and speaks of "the sons of Levi" making "unto the Lord an offering in righteousness" (3 Ne. 24:3). This is Jesus quoting the post-exilic Book of Malachi. The Nephites had not had this book before (3 Ne. 26:2), so there is no indication that they knew anything about the Levites' special role in the cult of animal sacrifice until after the visit of Jesus -- by which point, of course, said cult had been terminated by Christ (3 Ne. 9:19).
So for me the simplest solution is that Moses never instituted a priesthood restricted to descendants of his brother Aaron, that that was a much later innovation. For what it's worth, this is in broad harmony with the consensus of secular textual critics of the Bible (not a group I ordinarily put a great deal of stock in), who generally date the so-called "Priestly" material in the Torah to the late neo-Babylonian or even Persian period, well after the time of Lehi.
