The unique perspective of the Gospel of Luke is best illustrated in the Parable of the Prodigal Sons (Luke 15:11-32). In this familiar story, there are two sons whose lives have different outcomes. The lost son becomes repentant, returns home, and is welcomed back with lavish compassion. The "righteous" son stays home and grouses at the compassion given to his brother.
Other stories exclusive to Luke's Gospel display this same dichotomy. Consider the Pharisee and the Tax Collector (Luke 18), the Rich Man and Lazarus (Luke 16), the Good Samaritan (Luke 10), Mary and Martha (Luke 10), and the woman who washes Jesus' feet with her tears (Luke 7). In each, the outcasts are welcomed and declared righteous, and the "righteous" are exposed and shamed. It is the Gospel of unexpected righteousness.
OUTLINE OF LUKE
Week 1: Luke 1:1-4 - The overall purpose of Luke's composition
Skipping Luke 1:5-4:13 - Jesus' birth and John the Baptist's ministry
Luke 4:24-5:11 - Jesus has come to save outsiders
Week 2: Luke 5:12-6:49 - The "righteous" are blind to their need
Bring in Luke 10:25-37 (Good Samaritan) as an illustration
Week 3: Luke 7:1-9:50 - Profess your need and meet the real Jesus
Week 4: Luke 10:1-13:35 - Living in light of the Kingdom of God
Week 5: Luke 14:7-15:32 - Following Jesus to seek and save the lost
Week 6: Luke 16:19-19:27 - The marks of a follower of Jesus (examples)
Week 7: Luke 19:28-24:53 - Jesus is crucified, buried, raised, and ascends