The origins of this particular promise are interesting. Lehi certainly considers this a blessing that he has obtained:
"Wherefore, I, Lehi, have obtained a promise, that inasmuch as those whom the Lord God shall bring out of the land of Jerusalem shall keep his commandments, they shall prosper upon the face of this land; and they shall be kept from all other nations, that they may possess this land unto themselves. And if it so be that they shall keep his commandments they shall be blessed upon the face of this land, and there shall be none to molest them, nor to take away the land of their inheritance; and they shall dwell safely forever." (2 Nephi 1:9)
It is certainly this particular promise that Lehi is reiterating here in verse 4. However, the antecedents of this prophecy are much older. The earliest mention of this particular promise appears to be to Nephi:
"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 Nephi 2:20, See also 1 Nephi 4:14.)
Whether or not Lehi had also obtained this promise at that early date is unknown from the current Book of Mormon text. It certainly would not have been unusual for the Lord to have so prophesied to both Lehi and Nephi, but we have record only of Nephi's early promise.
Because the text we have as 1 Nephi and 2 Nephi are both written by Nephi for his own purposes, it is not surprising that it is the record of his receipt of the promise that is recorded rather than Lehi's.