Let's review what has happened to the tribes of Israel by the time of Nephi's writing. The twelve tribes of Israel each inhabited a specific portion of the land of Canaan, see map #5. The tribes were ruled by judges until the reign of the kings: Saul, David, and Solomon. After the reign of Solomon, the ten northern tribes, comprising all the tribes except the tribe of Judah and Benjamin, split from the two southern tribes. From this time forth, they were divided into the kingdom of Israel (also called the northern kingdom led by the tribe of Ephraim) and the kingdom of Judah (also called the southern kingdom led by the tribe of Judah), see map #9.
The scattering of Israel came because of the wickedness of the people. When Moses gave the law to the children of Israel, he also gave them a list of specific blessings and cursings which would take place depending on their obedience to the law. One of the curses listed is that they would be scattered by their enemies,
But it shall come to pass, if thou wilt not hearken unto the voice of the Lord thy God, to observe to do all his commandments and his statutes which I command thee this day; that all these curses shall come upon thee, and overtake thee….The Lord shall cause thee to be smitten before thine enemies: thou shalt go out one way against them and flee seven ways before them: and shalt be removed into all the kingdoms of the earth…And thou shalt become an astonishment, a proverb, and a byword, among all nations whither the Lord shall lead thee…And the Lord shall scatter thee among all people, from the one end of the earth even unto the other; and there thou shalt serve other gods, which neither thou nor thy fathers have known, even wood and stone. And among these nations shalt thou find no ease, neither shall the sole of thy foot have rest: but the Lord shall give thee there a trembling heart, and failing of eyes, and sorrow of mind (Deut 28:15, 25, 37, 64-5)
The scattering of Israel began with the Assyrian conquest of the northern kingdom. This occurred about 722 BC. The entire northern kingdom was destroyed and the people were taken to Assyria. This is how the ten tribes get lost. They are scattered by the Assyrians, and yet a body of them is preserved which remains as a cohesive body and is somehow led to the lands of the north. The Bible doesn't tell us much about what happened to them, In the ninth year of Hoshea the king of Assyria took Samaria, and carried Israel away into Assyria, and placed them in Halah and in Habor by the river of Gozan, and in the cities of the Medes. For so it was, that the children of Israel had sinned against the Lord their God (2 Kings 17:6-7). This is what Nephi is referring to when he says that the more part of all the tribes have been led away. In Nephi's day, the only tribes which were left were the tribe of Judah and Benjamin. There were a few in Jerusalem from the tribes of Ephraim, Manasseh, and Levi (see 1 Chron 9:3) but the vast majority of these three tribes had been taken north with the rest of the northern kingdom.