I then asked Grok, In the Book of Mormon who was the likely Cohen who could officiate the law of Moses?

In the Book of Mormon, there is no explicit mention of any person identified as a literal descendant of Aaron (a kohen or Cohen in the biblical sense) who had the specific right to officiate the full Law of Moses, including altar sacrifices, as required under the Torah for Aaronic priests.
Key Background from the Text and LDS Teachings

Lehi and his family were descendants of the tribe of Joseph (specifically Manasseh; see 1 Nephi 5:14; Alma 10:3). Nephi’s colony and the later Nephites were therefore not from the tribe of Levi, let alone the Aaronic line.
The Nephites (and later the people of Zarahemla/Mulekites) still kept the Law of Moses for centuries (e.g., Jarom 1:5; Mosiah 2:3; Alma 30:3; 3 Nephi 9:19–20). They offered sacrifices and burnt offerings “according to the law of Moses.”
Under the strict Law of Moses (as discussed in our previous exchanges), only Aaron’s direct male descendants (kohanim) could officiate at the altar and perform the core priestly duties. Other Levites assisted, and non-Levites were not authorized.

The Book of Mormon does not name or identify anyone as a Cohen/kohen or a literal son of Aaron who held that exclusive right.

Who Performed Priestly Duties Among the Nephites?

The text describes priests and high priests who taught, baptized, administered ordinances, and led worship — but their authority is presented as coming from God (often described as “after the order of the Son of God” or Melchizedek Priesthood), not strictly from Aaronic lineage.
Notable figures include:

Nephi (and his brothers Jacob and Joseph) — Nephi consecrated his brothers as priests (2 Nephi 5:26).
King Mosiah (and earlier kings in the line of Nephi) — They functioned as both political and religious leaders.
Alma the Elder — A former priest under the wicked King Noah who repented, baptized at the Waters of Mormon, and was later recognized by King Mosiah as having authority from God (Mosiah 18; 23:16–17). Alma is described as a descendant of Nephi (Mosiah 17:2), not Levi or Aaron.
Alma the Younger and other Nephite leaders — They operated under higher (Melchizedek) priesthood authority.

LDS scholars and official teachings note that the Nephites appear to have operated under the Melchizedek Priesthood (the higher priesthood), which allowed worthy men outside the tribe of Levi to officiate in teaching, baptism, and other ordinances once the full gospel was understood. The lineal restrictions of the Aaronic Priesthood for altar service were effectively lifted or superseded in the Nephite record because the law of Moses was fulfilled in Christ (see 3 Nephi 9:19–20; also the Bible Dictionary entry on Aaronic Priesthood in LDS scriptures).
Why No Mention of a Cohen?
The Book of Mormon does not resolve the apparent tension by identifying a hidden Aaronic descendant among Lehi’s group or the Mulekites. Instead, it emphasizes authority from God through prophets and righteous leaders rather than strict tribal lineage for the lesser priesthood functions.
In summary:
There is no named individual in the Book of Mormon who is presented as a Cohen (direct descendant of Aaron) with the exclusive right to officiate the Law of Moses sacrifices in the biblical sense. The Nephite priests and leaders exercised their ministry through divine calling and Melchizedek Priesthood authority, even while observing the outward performances of the law until Christ’s visit.
If you’re asking because of the D&C teachings on literal descendants of Aaron having a right to the bishopric (presidency of the Aaronic Priesthood), note that the Book of Mormon itself does not apply or demonstrate that specific lineal claim. The text focuses more on faith, repentance, and authority “from on high.”

Zoram

Grok continues, “It makes sense that Zoram was the likely Cohen or descendant of Levi. Nephi knew he needed to bring Zoram on the journey to the promised land as the Nephites practiced the law of Moses from 600 BC until Christ came to fulfill that need. Your theory—that Zoram was likely a descendant of Levi (or even a Kohen/Cohen with Aaronic rights) and that Nephi deliberately brought him along to enable proper observance of the Law of Moses—is a popular speculation among some Book of Mormon readers and independent LDS researchers, but it is not official doctrine of the Church of Jesus Christ of Latter-day Saints, nor is it stated or clearly implied in the text itself.

What the Book of Mormon Actually Says About Zoram

Zoram is introduced simply as “the servant of Laban” who had charge of the brass plates (1 Nephi 4:20, 31–38).
He swore an oath to join Lehi’s family, traveled with them, married one of Ishmael’s daughters, and remained a faithful friend to Nephi (1 Nephi 4:35–37; 2 Nephi 1:30–32).
Lehi blessed him equally with his own sons, promising that his seed would be blessed if he remained faithful.
His descendants became one of the distinct groups among Lehi’s people, known as Zoramites (Jacob 1:13), who later largely apostatized and often allied with the Lamanites.

The text never mentions Zoram’s tribal lineage, family background, or any priestly role. Laban himself (Zoram’s master) was a descendant of Joseph (Manasseh), like Lehi (1 Nephi 5:14–16). No verse identifies Zoram as a Levite or Aaronic descendant.

Why Some Readers Speculate Zoram Was a Levite

This idea appears in blogs, forums, and some scholarly speculations for these reasons:

Zoram had access to the brass plates (which contained the Law of Moses, genealogy, and sacred records) and held “the keys of the treasury.”
Nephi went to great lengths to bring Zoram on the journey rather than leaving him behind.
The Nephites strictly observed the Law of Moses (including sacrifices and burnt offerings) for over 600 years until Christ fulfilled it (e.g., Mosiah 2:3; Alma 30:3; 3 Nephi 9:19–20).
Under the strict biblical Law of Moses, only Aaron’s descendants (kohanim) could officiate at the altar for most sacrifices.

Some propose Zoram was a Levite servant/refugee attached to Laban’s household, possibly as a record-keeper or guardian of sacred items. A few even suggest he could have provided the necessary Aaronic lineage for proper priestly officiation in the wilderness and New World.

The Mainstream LDS Scholarly and Doctrinal View

Most Church leaders and mainstream LDS scholars explain Nephite observance of the Law of Moses differently:

Lehi’s family (and the Mulekites who later joined them) had no Levites among them. They were primarily from the tribes of Joseph (Manasseh and Ephraim) and Judah (through Mulek).
The Nephites operated under the higher Melchizedek Priesthood (the priesthood “after the order of the Son of God”), which allowed worthy non-Levites to officiate in teaching, baptism, and even sacrifices when necessary.
Lehi himself offered sacrifices shortly after leaving Jerusalem (1 Nephi 2:7; 5:9), and Nephi consecrated priests and teachers from among his people (2 Nephi 5:26).
President Joseph Fielding Smith and others taught that the Nephites did not officiate under the Aaronic Priesthood in the lineal sense. The Melchizedek Priesthood gave them authority to perform the required ordinances of the law while they waited for the coming of Christ.

In short, the Book of Mormon does not resolve the “who officiated the sacrifices?” question by introducing a hidden Levite or Cohen. It simply shows that God accepted their worship through prophetic authority and the higher priesthood.

Bottom Line

Your idea is an interesting and thoughtful attempt to reconcile the strict requirements of the Law of Moses with the Nephite record. It has circulated for years in some Latter-day Saint circles. However, the text itself is silent on Zoram’s ancestry, and official teachings emphasize that the Nephites functioned under Melchizedek Priesthood authority rather than needing a literal Aaronic descendant to “make it legal.”

Nephi’s insistence on bringing Zoram seems more directly tied to:

Securing the brass plates (essential for preserving the scriptures and genealogy).
Preventing Zoram from alerting Laban’s household or the authorities in Jerusalem.

If Zoram had been a Levite or Cohen, the Book of Mormon’s authors (who were careful about genealogy and priesthood matters) would almost certainly have mentioned it, just as they recorded Lehi’s descent from Joseph.” Grok AI May 16, 2-26

In my personal opinion, I believe it is very likely that Zoram was indeed of the tribe of Levi. It makes sense as to why Nephi felt it so important to bring him along in the wilderness. Below are other similar opinions.

“ZORAM WAS A LEVITE… Zoram had the ‘keys of the treasury’ and… could go ‘into the treasury’… In ancient Israel there were divisions of gatekeepers… The Levites and their tribe had charge of the treasures of the House of God… That Zoram had the ‘keys of the treasury’… tells us he was not an ordinary house slave… As levitical priest both Zoram and his male descendants could have functioned in their roles as priests as required by God in the Torah of Moses.” It ties this to 1 Chronicles 26:20 and examples like Micah’s Levite priest (Judges 17).” Source

Alan C. Miner (in commentary on 1 Nephi 4:20, 35): “Gordon Thomasson hypothesizes that Zoram was a Levite refugee from the Northern Kingdom, attached to Laban’s household through generations of service (not for keep-servitude) to his tribe, thus accounting for his (ritual?) responsibility [with] the plates and the appearance of what are possibly Levitical ordinances in Lehi’s camp…” Source

“Broader scholarly context (e.g., John L. Sorenson and others in discussions of the “seven tribes”): Lehi’s blessings treat Zoram’s line as a distinct tribe alongside those from Lehi’s sons. Some note the absence of an explicit Levite line in the Book of Mormon and speculate Zoram (or similar figures) could fill that functional role for Law of Moses observance, though others argue non-Levites could perform certain duties in the Nephite context or that the text simply does not detail it.” Source