I was sent only to the lost sheep of the house of Israel

Lord Jesus Christ started the ministry with the good news that he came for entire world and not just for the house of the Israel - But I tell you truly, many widows were in Israel in the days of Elijah, when the heaven was shut up three years and six months, and there was a great famine throughout all the land; but to none of them was Elijah sent except to Zarephath, in the region of Sidon, to a woman who was a widow. And many lepers were in Israel in the time of Elisha the prophet, and none of them was cleansed except Naaman the Syrian. So all those in the synagogue, when they heard these things, were filled with wrath, and rose up and thrust Him out of the city; and they led Him to the brow of the hill on which their city was built, that they might throw Him down over the cliff. Then passing through the midst of them, He went His way - Luke 4:25-30

Then why Jesus Christ said, I was sent only to the lost sheep of the house of Israel?

First we need to understand how Jacob got the name Israel, when we read these versus, its appears as Jacob got the name Israel by his physical strength - And Jacob was left alone. And a man wrestled with him until the breaking of the day. When the man saw that he did not prevail against Jacob, he touched his hip socket, and Jacob's hip was put out of joint as he wrestled with him. Then he said, Let me go, for the day has broken. But Jacob said, I will not let you go unless you bless me. And he said to him, What is your name? And he said, “Jacob.” Then he said, “Your name shall no longer be called Jacob, but Israel, for you have striven with God and with men, and have prevailed.” Then Jacob asked him, “Please tell me your name.” But he said, “Why is it that you ask my name?” And there he blessed him. So Jacob called the name of the place Peniel, saying, “For I have seen God face to face, and yet my life has been delivered - Genesis 32:24-30

But the truth is, Jacob wept and pleading for Lord's favor whole night and got the name Israel - The Lord has an indictment against Judah and will punish Jacob according to his ways; he will repay him according to his deeds. In the womb he took his brother by the heel, and in his manhood he strove with God. He strove with the angel and prevailed; he wept and sought his favor. He met God at Bethel, and there God spoke with us, the Lord, the God of hosts, the Lord is his memorial name - Hosea 12:2-5

So "lost sheep of the house of Israel" means the one who trust Lord and desperately seeks his favor with humbleness.

And It could be around 80 miles walk for Jesus Christ to visit the region of Sidon, But He came all the way for the one lost sheep of the house of Israel, that is the Canaanite women - And Jesus went away from there and withdrew to the district of Tyre and Sidon. And behold, a Canaanite woman from that region came out and was crying, “Have mercy on me, O Lord, Son of David; my daughter is severely oppressed by a demon.” But he did not answer her a word. And his disciples came and begged him, saying, “Send her away, for she is crying out after us.” He answered, “I was sent only to the lost sheep of the house of Israel.” But she came and knelt before him, saying, “Lord, help me.” And he answered, “It is not right to take the children's bread and throw it to the dogs.” She said, “Yes, Lord, yet even the dogs eat the crumbs that fall from their masters' table.” Then Jesus answered her, “O woman, great is your faith! Be it done for you as you desire.” And her daughter was healed instantly. Jesus went on from there and walked beside the Sea of Galilee. And he went up on the mountain and sat down there - Matthew 15:21-29