The House of Israel will not be reestablished until the Ten Tribes have returned and the Time of the Gentiles is fulfilled. Some latter-day Saints are literal descendants of the Tribes of Israel but their true gathering by the Lord is yet to be.
During these latter-days, people here in America, also speak of this land as if it is ours forever, a land consecrated for our gain. “This land is our Land” is nothing more than a hopeful cry but once again what do the scriptures say? This land, the “Promised Land,” is not ours, “But behold, this land, said God, shall be a land of thine inheritance, and the Gentiles shall be blessed upon the land” (2 Nephi 10:10). We are blessed here and we have prospered but we must remember that it is only for a season . . .
1 Nephi 13:15
And I beheld the Spirit of the Lord, that it was upon the Gentiles, and they did prosper and obtain the land for their inheritance; and I beheld that they were white, and exceedingly fair and beautiful, like unto my people before they were slain. (Emphasis added in bold)
Nevertheless, thou beholdest that the Gentiles who have gone forth out of captivity, and have been lifted up by the power of God above all other nations, upon the face of the land which is choice above all other lands, which is the land that the Lord God hath covenanted with thy father that his seed should have for the land of their inheritance; wherefore, thou seest that the Lord God will not suffer that the Gentiles will utterly destroy the mixture of thy seed, which are among thy brethren. Neither will he suffer that the Gentiles shall destroy the seed of thy brethren. (Emphasis added in bold)
1 Nephi 10:19
Wherefore, I will consecrate this land unto thy seed, and them who shall be numbered among thy seed, forever, for the land of their inheritance; for it is a choice land, saith God unto me, above all other lands, wherefore I will have all men that dwell thereon that they shall worship me, saith God. (Emphasis added in bold)
TPJS Section One 1830-34 Pg.17 Zion and Jerusalem
The Book of Mormon is a record of the forefathers of our western tribes of Indians; having been found through the ministration of a holy angel, and translated into our own language by the gift and power of God, after having been hid up in the earth for the last fourteen hundred years, containing the word of God which was delivered unto them. By it we learn that our western tribes of Indians are descendants from that Joseph who was sold into Egypt, and that the land of America is a promised land unto them, and unto it all the tribes of Israel will come, with as many of the Gentiles as shall comply with the requisitions of the new covenant. (See also Doctrine and Covenants 45:24–25) (Emphasis added in bold)
3 Nephi 20: 15–16
And I say unto you, that if the Gentiles do not repent after the blessing which they shall receive, after they have scattered my people– Then shall ye, who are a remnant of the house of Jacob, go forth among them; and ye shall be in the midst of them who shall be many; and ye shall be among them as a lion among the beasts of the forest, and as a young lion among the flocks of sheep, who, if he goeth through both treadeth down and teareth in pieces, and none can deliver.
The LDS Church will not even build the New Jerusalem as many of them would hope
(3 Nephi 21:22–24). In the book titled The Articles of Faith we can see this doctrine laid out in both black and white: the Gentiles, if repentant, are to be permitted to assist the house of Israel in building the city to be called the New Jerusalem–3 Nephi 21:14–24. (AOF, Ch.19, Pg.355)