Why did he send Paul to the Gentiles then?
The lost sheep of the house of Israel consists of Judah the Jews, and Ephraim scattered among the Gentiles.
Acts 1 (ESV)
6 So when they had come together, they asked him, "Lord, will you at this time restore the kingdom to Israel?" 7 He said to them, "It is not for you to know times or seasons that the Father has fixed by his own authority. 8 But you will receive power when the Holy Spirit has come upon you, and you will be my witnesses in Jerusalem and in all Judea and Samaria, and to the end of the earth."
John 11 (ESV)
47 So the chief priests and the Pharisees gathered the council and said, "What are we to do? For this man performs many signs. 48 If we let him go on like this, everyone will believe in him, and the Romans will come and take away both our place and our nation." 49 But one of them, Caiaphas, who was high priest that year, said to them, "You know nothing at all. 50 Nor do you understand that it is better for you that one man should die for the people, not that the whole nation should perish." 51 He did not say this of his own accord, but being high priest that year he prophesied that Jesus would die for the nation, 52 and not for the nation only, but also to gather into one the children of God who are scattered abroad. 53 So from that day on they made plans to put him to death. 54 Jesus therefore no longer walked openly among the Jews, but went from there to the region near the wilderness, to a town called Ephraim, and there he stayed with the disciples.