These twelve Jesus sent out, instructing them, "Go nowhere among the Gentiles and enter no town of the Samaritans, but go rather to the lost sheep of the house of Israel."
Matthew 10:5-6

The "lost sheep of the house of Israel" were not to be found among the gentiles or Samaritans, but only among the Jews. The Samaritans were a mix of Canaanites, Israelites, and other foreign peoples relocated to the land by the ancient Assyrian Empire. This means that the "lost sheep of the house of Israel" in this context can only refer to the Jews (people who knew the Scriptures and identified themselves as Jews) and not to Israelites who had been scattered and absorbed by the nations nor to gentile converts.