Matthew 10:6, Lost sheep of the house of Israel. The phrase the house of Israel has several possible meanings depending on the context of the surrounding verses in which it is found.
The phrase the house of Israel is used 146 times in the Scriptures. Prior to the division of the united kingdom after the death of Solomon, this phrase referred to all twelve tribes of Israel. Afterwards (during the time of the prophets), it was used in contradistinction to the phrase “house of Judah” in reference to the Northern Kingdom.
In the Testimony of Yeshua, Yeshua makes reference to the “lost sheep of the house of Israel” (Matt 10:6; 15:54). Elsewhere in the Testimony of Yeshua this term refers to all twelve tribes of Israel (Acts 2:36; 7:42; Heb 8:10), and in some references it refers to just the Northern Kingdom (Heb 8:8). The context of the passage of scripture surrounding this phrase determines its meaning.
Although this phrase can include all the tribes of Israel and not just the Jews who were largely from the tribe of Judah, in Matthew 10:6, Yeshua seems to equate the lost sheep of the house of Israel with the Jews who were living in the land of Israel in his day, and not to the rest of the Israelite tribes who were at that time scattered among the Gentile nations. It was Yeshua’s priority to take the gospel message first to the Jews in Jerusalem and Judea, and then to the rest of the world, and he expected his disciples to follow this same pattern (Acts 1:8).
In the larger sense, the Scriptures reveal that all of YHVH’s people have been like sheep that have gone astray spiritually, every man to his own way, because of sin (Isa 53:6). So in the broadest sense, this phrase refers to all the tribes of Israel including Gentiles with which they have mixed themselves through intermarriage.
Eventually, the gospel message is for everyone universally. Yeshua demonstrated this when, on several occasions, he ministered to non-Jewish Gentiles including preaching the gospel message to the Samaritan woman in John chapter four.