Ezekiel 34 says the LORD himself will search for, rescue, and shepherd his lost sheep.
What Luke 15 portrayed in parable Jesus now states directly as the Son of Man's mission: he came to seek and save the lost.
Jesus assumes the saving shepherd mission promised of God, making this a particularly strong Lukan divine-identity connection.
Zacchaeus receives Jesus joyfully and responds with repentance and restitution.
His transformed response illustrates the salvation Jesus says has come to the house.