Between 1047 B.C. and 931 B.C., the 12 tribes of the nation of Israel thrived under Kings Saul, David, and then King Solomon. But towards the end of Solomon's reign, he fell into idolatry and God prophesied of the tearing apart of the Kingdom as judgment for these sins.
1st Kings 11:10-12
"And had commanded him concerning this thing, that he should not go after other gods: but he kept not that which the LORD commanded.
Wherefore the LORD said unto Solomon, Forasmuch as this is done of thee, and thou hast not kept my covenant and my statutes, which I have commanded thee, I will surely rend the kingdom from thee, and will give it to thy servant.
Notwithstanding in thy days I will not do it for David thy father's sake: but I will rend it out of the hand of thy son."
And as Prophesied, upon the death of King Solomon in 931 B.C., the Children of the northern tribes of Israel rebelled against Solomon's son Rehoboam, and followed Jeroboam. Thus the nation was divided into two kingdoms, north and south.
1st Kings 12:20-21
"And it came to pass, when all Israel heard that Jeroboam was come again, that they sent and called him unto the congregation, and made him king over all Israel: there was none that followed the house of David, but the tribe of Judah only.
And when Rehoboam was come to Jerusalem, he assembled all the house of Judah, with the tribe of Benjamin, an hundred and fourscore thousand chosen men, which were warriors, to fight against the house of Israel, to bring the kingdom again to Rehoboam the son of Solomon.
Judah and the tribe of Benjamin were the only tribes that remained loyal to Solomon's son Rehoboam, and these two tribes of the southern area became known as the kingdom of Judah (because Judah was the principle tribe). The 10 tribes to the north who were disloyal to Rehoboam, set up a separate kingdom under Jeroboam (who was not in the kingly line of the House of David). These Northern tribes became known as Israel, or in some instances Ephraim (because it was the principle tribe). For the next two centuries the people were divided into these two Kingdoms, yet almost immediately a remnant of the tribes to the north began to return to the southern Kingdom (because King Jeroboam turned the Northern Kingdom to idol worship). It is clear that the Levites and many of the other tribes who eschewed this evil, returned to what was now called Judah.
2nd Chronicles 11:14-17
"For the Levites left their suburbs and their possession, and came to Judah and Jerusalem: for Jeroboam and his sons had cast them off from executing the priest's office unto the LORD:
And he ordained him priests for the high places, and for the devils, and for the calves which he had made.
And after them out of all the tribes of Israel such as set their hearts to seek the LORD God of Israel came to Jerusalem, to sacrifice unto the LORD God of their fathers.
So they strengthened the kingdom of Judah, and made Rehoboam the son of Solomon strong, three years: for three years they walked in the way of David and Solomon."
Clearly, a remnant was returning to the house of David from Israel. When King Asa began to reign in 911 B.C., he turned again the hearts of the people to the Lord and did not the evil of his father. By 896 B.C., after Asa put away the idols out of all the land, even those who were not Hebrew came with them to the southern Kingdom out of the tribes of Ephraim, Manasseh, and Simeon. Again, there was a remnant returning, not the whole tribe.
2nd Chronicles 15:9-10
"And he gathered all Judah and Benjamin, and the strangers with them out of Ephraim and Manasseh, and out of Simeon: for they fell to him out of Israel in abundance, when they saw that the LORD his God was with him.
So they gathered themselves together at Jerusalem in the third month, in the fifteenth year of the reign of Asa."
So it is pretty clear that a remnant from Israel was coming back to be under rule of the House of David. But the abomination of the northern tribes of Israel which started with Jeroboam, continued with his children and would not go unpunished by God. God sent the promised judgment to cut them off and cast them out of His sight.
2nd Kings 17:22-23
"For the children of Israel walked in all the sins of Jeroboam which he did; they departed not from them;
Until the LORD removed Israel out of his sight, as he had said by all his servants the prophets. So was Israel carried away out of their own land to Assyria unto this day."
And in 722 B.C., Assyrian King Shalmaneser V, who ruled the vast empire to the north, invaded the Kingdom of Israel and subjugated  them. The Israelite inhabitants were exiled and dispersed into the outlying general area (what is today Syria, Iran and Iraq), as was the tradition of the Assyrians to prevent rebellion or revolt. But again, as prophesied, a portion of the tribes of Israel returned to Judah, as in B.B. 716. King Hezekiah who reigned in Judah now, called for the remnant to return.
2nd Chronicles 30:6
"So the posts went with the letters from the king and his princes throughout all Israel and Judah, and according to the commandment of the king, saying, Ye children of Israel, turn again unto the LORD God of Abraham, Isaac, and Israel, and he will return to the remnant of you, that are escaped out of the hand of the kings of Assyria.
2nd Chronicles 30:10
10 So the posts passed from city to city through the country of Ephraim and Manasseh even unto Zebulun: but they laughed them to scorn, and mocked them.
Nevertheless divers of Asher and Manasseh and of Zebulun humbled themselves, and came to Jerusalem."
Quite obviously (according to God) though these tribes were dispersed, they were neither lost, nor unaccounted for in God's Word. The wicked of them dispersed into the nations who mocked. They would not return, thus were cut off of God and eventually assimilated into the surrounding nations. But the remnant who humbled themselves before Hezekiah's call, did return. One would have to hold an irrational inherent bias in order to agree that portions of the northern tribes (Ephraim, Manasseh, Asher, Zebulon, Issachar) did come to Jerusalem for Passover, yet still insist that the tribes were still lost. That makes no sense at all. There is no mystery. A 'remnant' was restored (as was prophesied) to Judah. It was never meant for all the people people to return. It was never God's plan or Word of prophesy, to restore the whole people. The tribes returned as God intended, and were accounted for. And this can be very easily proven by scripture. In 633 B.C. in the 8th year of the reign of King Josiah, he walked after the way of the good kings and cleansed the "tribal cities" of the nation Judah.
2nd Chronicles 34:5-7
"And he burnt the bones of the priests upon their altars, and cleansed Judah and Jerusalem.
And so did he in the cities of Manasseh, and Ephraim, and Simeon, even unto Naphtali, with their mattocks round about.
And when he had broken down the altars and the groves, and had beaten the graven images into powder, and cut down all the idols throughout all the land of Israel, he returned to Jerusalem."
2nd Chronicles 34:9
"And when they came to Hilkiah the high priest, they delivered the money that was brought into the house of God, which the Levites that kept the doors had gathered of the hand of Manasseh and Ephraim, and of all the remnant of Israel, and of all Judah and Benjamin; and they returned to Jerusalem."
Again, the tribes neither lost nor unaccounted for in God's Word. Israel that transgressed were 'cut off,' but 'the remnant' returned. And likewise when Judah transgressed the laws of God as her sister Israel had, God also sent judgment against her and the land was invaded and conquered by the Chaldean King Nebuchadnezzar some 136 years later. He destroyed their house and carried the people away captive into Babylon. The Temple was destroyed and they were subjugated until 539 B.C. when Babylon itself fell to King Cyrus of the Medes and Persians. Under Cyrus, again the remnant of exiled 'Jews and Israelites' returned to Jerusalem and construction on the Temple started. And later in 458 B.C., Ezra returned to Jerusalem with more of the exiled Jews to reestablish the law. Both the house of Israel and Judah were represented in the remnant reestablished in Judah. Israel and Judah were now one people.
So any gibberish about the ten "lost" tribes is a fake, bogus claim, simmilar to plenty of other counterfeit claims which allegedly "expand" or fill the alleged "gaps" of the Old Testament. And it is not surprising that vertually all of these non-Biblical stories of Biblical characters are at one time or another concoted and derived from the late-arrival: the Talmud. There never is, nor ever was a group of ten tribes that got "lost"... except of-course in the braincells of the apostles of the Synagogue of Satan. The primary purpose of propagating this folly is it's use for the Talmudic Rabbis as an alibi for converting anybody they fancy (turning non-jewish/non-middle-eastern folk into "jews", as they did and still are doing like the case of the Turks, Kurds, Khazars, Indians, Baghdadis, Georgians, Ethiopians... etc.