In the record of the small plates, it is Nephi, not Lehi, who gives the first notice of this promise: “And inasmuch as ye shall keep my commandments, ye shall prosper, and shall be led to a land of promise; yea, even a land which I have prepared for you; yea, a land which is choice above all other lands” (1 Ne. 2:20; see also 1 Ne. 4:14). Lehi was aware of this prophecy at least by the time he sent his sons for the brass plates (1 Ne. 5:5). It would not be unusual for Yahweh to make the same promise to both prophets, but we would expect that it came first and officially to Lehi. Although Nephi records his own prophecy first, I suggest that it was first given to Lehi as the patriarch.
Note that the information that Yahweh had kept other nations from knowledge of the land “as yet” (v. 8) leads directly into the Nephite foundational promise (in this verse). If we read these verses in the context of known history, the “as yet” defines the conditions into which the Lehites landed. There was a population in the land, but no foreign conqueror “as yet.” I suggest that this promise comes because of the implicit reality that other nations would indeed come, and would attempt to overrun Lehi’s descendants. Lehi receives a promise that they will be protected from those other nations upon condition of their righteousness. This is a promise that is of no value unless others do come and threaten the Nephites. Therefore, it is best read as a means of continuing the fortuitous circumstances they find upon arrival, but which will not last.
This is certainly the way that the Nephites understood the promise. Note how the promise appears as early as Jarom: “And thus being prepared to meet the Lamanites, they did not prosper against us. But the word of the Lord was verified, which he spake unto our fathers, saying that: Inasmuch as ye will keep my commandments ye shall prosper in the land” (Jarom 1:9; emphasis mine).
Less than two hundred years after Lehi receives the promise, Jarom is reporting that it has already been verified in a conflict with the Lamanites. This use of the promise will continue throughout the Book of Mormon. The Nephites consistently applied it to conflicts with the Lamanites and consistently saw it in terms of their current conditions, not as a far-off prophecy of the coming of the Europeans. Ironically, it is only the modern reader who withholds the fulfillment of the negative part of this promise until Columbus arrives in 1492, nearly 1100 years after the Nephites had already been destroyed by “other nations” who overran them because of their faithlessness.
Reference: This promise is cited at least thirteen more times in the Book of Mormon, but its quoters probably refer to the book of Lehi as a source, not to the book of 2 Nephi, unless, of course, the identical wording appeared in both sources. Still, Mormon’s abridgment no doubt drew on the book of Lehi, and he apparently did not use the small plates at all as a source for his abridgment.