No. The woman in Matt. 15:22-25 is from the land of Canaan, from the coastal region of northwest Palestine; therefor not of the lineage of Abraham. Mark's account (Mk. 7:24-28) calls her a Greek, or Syrophenician.
The "lost sheep of the house of Israel" did not refer to a physical location of unknown people. They were lost spiritually, not understanding the kingdom, nor the truth of God's word. Christ was the messenger, the Angel of the Lord, the Word sent to bring the good news of reconciliation.
Christ was speaking to His disciples in Matt. ch. 10 giving them instructions for their mission journey throughout the "cities of Israel".
"5These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not: 6 But go rather to the lost sheep of the house of Israel." (Matt. 10:5-6, KJV)
"23 But when they persecute you in this city, flee ye into another: for verily I say unto you, Ye shall not have gone over the cities of Israel, till the Son of man be come.“ (Matt. 10:23, kJV)
He sent His disicples to the existing cities of those days to seek out those of the diaspora. Having determined that Christ was speaking to His disciples before His crucifixion, we can know that the instructions He gave them in this chapter were specifically for them. The “lost sheep of the house of Israel” were not lost in the sense that no one knew where they were. God and Jesus knew where they were. The Sanhedrin knew where they were as those of the Assyrian and Babylonian dispersions (diaspora) had settled throughout Asia and were sending their “tithes” to the council in Jerusalem.
The disciples therefore knew where Christ was sending them.
“Peter, an apostle of Jesus Christ, to the strangers scattered throughout Pontus, Galatia, Cappadocia, Asia, and Bithynia,” (1 Pet. 1:1, KJV)
Peter was speaking to the “strangers,” those of the dispersion still living outside of Judea and Jerusalem, in Pontus, Galatia, Cappadocia, Asia, and Bithynia. I am sure there were those of other nations (gentiles) in those congregations, but primarily Peter was sent to the spiritually lost of the tribes of Israel to preach the gospel of Christ.
The instructions Christ gave His disciples in Matt. chap. 10 are not instructions for all men of all generations, as many of those cities of the “lost tribes of Israel” no longer exist. Pontus was located on the southern coast of the Black Sea, and today is part of the territory of Turkey. Cappadocia (Kapadokya) is a region in Turkey that contains many villages and cities. Galatia was a city in what is now called Turkey, bounded on the north by Bithynia and Paphlagonia, and on the south by Lycaonia and Cappadocia, on the east by Pontus, and the west by Phrygia.
These cities existed in the first century AD. When Christ told His disciples that they would not finish going through them before He returned, then we know that He returned in that generation before the disciples could finish going through those cities.
Christ personally preached to the Samaritans in Matt. 15. They were part of the diaspora, half Jew and half gentile from the Assyrian captivity, so they were included in those spiritually "lost sheep" that needed to hear the gospel. But, Christ knew exactly where they were living.
Those were specific instructions to His disciples of that generation of the first century AD to the then known cities of the diaspora (Israel) to preach the gospel, the good news that the Messiah had come.