We know from the scriptures that Gentiles who enter into covenants are numbered among the house of Israel. What I hadn't really noticed before is what we read in 1 Nephi 14:1-2
1 And it shall come to pass, that if the Gentiles shall hearken unto the Lamb of God in that day that he shall manifest himself unto them in word, and also in power, in very deed, unto the taking away of their stumbling blocks—
2 And harden not their hearts against the Lamb of God, they shall be numbered among the seed of thy father; yea, they shall be numbered among the house of Israel; and they shall be a blessed people upon the promised land forever; they shall be no more brought down into captivity; and the house of Israel shall no more be confounded.
Here it is specified that the Gentiles shall not only be numbered among the house of Israel, but among the seed of Lehi (who was of the house of Israel). We learn from Alma 10:3 that Lehi was from the tribe of Manasseh. So what is all this talk about Ephraim? In a discourse delivered in Logan, Utah 6 May 1882, Apostle Erastus Snow said
The Prophet Joseph Smith informed us that the record of Lehi was contained on the 116 pages that were first translated and subsequently stolen, and of which an abridgment is given us in the First Book of Nephi, which is the record of Nephi individually; he himself being of the lineage of Manasseh; but that Ishmael was of the lineage of Ephraim
There is some uncertainty about it, but matrilinearity (the practice of tracing Israelite descent through the maternal line) may have been practiced at Lehi's time. In that case, Lehi's seed became Ephraim when his sons married Ishmael's daughters. We also know that Nephi had sisters, who may have married grandchildren of Ishmael. (1 Nephi 7:6 shows that Ishmael already had married sons when they left Jerusalem)
the two sons of Ishmael and their families
In any case, there is a mix of Ephraim and Manasseh in the Nephite and Lamanite peoples, which explains the heavy emphasis on Joseph in the Book of Mormon, who was the father of both. People from Gentile nations living today to witness the "fulness of the Gentiles" unfold, who enter into the covenants offered by the restored church, are often told in their patriarchical blessings that they are numbered among Ephraim, which is Lehi's seed. Just as we know Ephraim was told in his patriarchical blessing that the fulness of the Gentiles in these latter days would come through his seed.