While Jesus is describing, generally, the dispersal of primarily the three tribes ("The Jews", 'Judah), there is evidence that there were members of other tribes besides the descendants of the Southern Kingdom were in contact with the Southern kingdom in the time of Josiah:
Here are the verses on that:
2 Chron. 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.
This occurs in the time of Josiah, which is well after the invasions that exiled the Northern Kingdom in the time of Ahaz and Hezekiah (2 Kings 18). The only logical conclusion is that some settlements of Israelites were known to the Levites at that time. The book of Tobit would attest to this - Tobit dwelled in Ecbactana, a city of the Medes.
During the time near Jesus' birth, Luke 2:36 attests to Hanna of the tribe Asher, so we have evidence that at least one Israelite from the 12 tribes made in back to Jerusalem to worship at the Temple (most all her life, apparently)
So, when James states in the first verse of his epistle "to the 12 tribes scattered abroad" it seems that these tribes were not 'lost' as we understand them today, but were in a process of re-assimilation into their heritage, a process that continues until this day.
According to Josephus, James died between the procuratorships of Festus and Albinus, so in about 60-61 A.DJosephus sourceJewish Encylopedia, Albinus.
Therefore, at the time of James, the 12 tribes, including Judah, were scattered abroad (Judah being scattering in the Babylonian exile, and never fully leaving exile). However, a (large) remnant of both Judah and a 'small' remnant of 'Ephraim' was still in Jerusalem. So, at the end of the day, this statement can't apply to just Judah unless Anna was the absolute last Northern tribes Israelite to come to Jerusalem, which seems unlikely given the more than 500 year gap between Josiah's time and hers. It doesn't seem likely that the remnant of Ephraim would cease to trickle into Jerusalem for some reason, unless it was destroyed, but would that end their contact with the Jewish people. I don't think so.
It was around Passover that Jerusalem was sieged, so a smattering of Israelites from Northern tribes from abroad were most likely there, albeit in proportionally smaller numbers than Judaens.
This passage is clearly referring to the house of Judah (Benjamin, Judah, and Levi) + the 'small' remnant of the Northern house of Israel. It is doubtful that many from any other tribes were dwelling permanently in the land of Israel, though some clearly were. The future return of these tribes, and even Judah's complete return, has yet to happen, though Jews have returned to their land in part. Still, bit more than half are not there, and most of the tiny remnant of the faithful feast-goers among the Northern Tribes has been assimilated into the Jewish people, or killed in 70 AD (my hypothesis). That leaves the future fulfillment of Hosea 1:10, where the people who has literally lost its heritage finds it again, and return en masse to the land of Israel.
It is reasonable to assume that the tiny remnant that did still go to Jerusalem for the feasts was wiped out in 68 - 70 AD though a community of Notsrim was in Pella and other Jews in Javnia (rabbinates) continued to exist in pockets near the land of Israel (Galil and Perea) Flight to Pella. So, 70 AD seems like a date we lost track of the last vestiges of these people...unfortunately the rabbis claim them as permanently lost, acccording to Shabbat 101b in the Talmud, and Rashi (found on https://www.chabad.org/library/article_cdo/aid/2500863/jewish/Where-Are-the-Ten-Lost-Tribes.htm).
If James wrote his letter before 61 AD, then he knew the impending destruction would not wipe on the congregations of Israelites abroad completely, and it was his hope that they would continue to be zealous for the law.
As history has shown, the sect of Jewish Christians who may have comprised of some Northern tribers was persecuted to the point of extinction and re-assimilation in the jewish religion. However, there are some in the mountains to the south of france and north of spain that can trace their ancestry back to these individuals, though I have only heard that from someone who said they'd been there, and have no source for you. Other claims about the lost tribes are hard to trace, but not without a grain of truth that God's people has been displaced far and wide. If the prophecies of total dispersion (Deut. 28) are true, is it not likely that many peoples would claim a blood connection to Israel without being Jewish?
For us to say to these nations, such as the Igbo of Nigeria, who believe themselves to be descendants of Gad, that they are 'lost' when they believe themselves to be true Israelites, is it grounded in Scripture? see link: