This short verse from Luke reveals Jesus motivation for coming to earth. The verse is spoken by Jesus after Zacchaeus is changed by Him coming to his house. Its valuable to realize the word "lost" was spoken by Jesus in the context of this individual person, Zacchaeus, who was called a sinner by others.
In the parable of the lost sheep in Luke 15:3-7, the man who has one lost sheep leaves the ninety nine who are in his care to find it. The mans heart longs for the one sheep to be safe in his care. Jesus continues the parable to say that when he finds the sheep " he lays it on his shoulders, rejoicing." This is a picture of Gods heart for individuals to be in His presence and care. At the end of the parable, Jesus says that there is more rejoicing in heaven over one who repents than others who need no repentance. There is more rejoicing over one who enters into the forgiveness of God, than those who already have it.
God longs for every unique person to be with him. Individuals are considered to be lost by God because of spiritual death that separates them from the everlasting life of God. The bible points out that death and sin are closely related.
For the wages of sin is death. Romans 6:23
And you were deadin your trespasses and sins. Ephesians 2:1
The sting of death is sin, and the power of sin is the law. 1 Corinthians 15:57
Sin is the thing that makes us lost and dead. Jesus seeks after the lost and loves them just like the man in the parable did for his lost sheep. To be brought back into the presence and care of God our sin needs forgiven and taken away. Jesus did this by offering Himself as a sacrifice for our sins on the cross, to remove the burden of sin that we couldn't. "Nothing but the blood" as the old Hymn says, is truly the only thing that can wash us white as snow and bring us into the presence of God. And to show that he conquered sin, the sting of death, Jesus rose to life victoriously in bringing us back to His fold. He loved and did this for individuals.