One thing that stood out to me from Luke’s Gospel (especially towards the beginning of it) were the numerous times Jesus seemingly defied others or what others thought was right. For example many of the miracles Jesus works are done on the Sabbath Day making it seem like he broke the commandment. But I think Luke does this on purpose and is trying to make a point by doing it.
In Luke’s Gospel, it says: “The Son of man is master of the Sabbath.” This shows that Luke is emphasizing the authority and power of God and the importance of doing good for others. This theme continues throughout portion of the Gospel where Jesus goes about teaching and healing.
Another part of the Gospel that I thought helped bring out this point was in Chapter 22 where Jesus tells of Peter’s fall and repentance. Instead of rebuking Peter after foretelling him denying him, Jesus chooses to show that he will recover and strengthen his brothers. By doing this, Luke again makes visible Jesus’s loving character that wants to heal and guide us.
Luke closes his Gospel by telling the story of the ascension. This is a fitting end because it closes with hope and healing. After the ascension it says the apostles went back to Jerusalem “full of joy.” By depicting this, Luke shows us that Jesus is continually among us and that his ‘leaving’ the world is not a cause for mourning because He is always with us.
John Seida 
I share your sentiments about the passage where Jesus forgives Peter despite his persistent denial. I find that Luke’s inclusion of this specific encounter serves to demonstrate the eternal mercy of Jesus as our Lord and Savior. No matter how many times we sin against God, Jesus is willing to forgive us if we repent and persevere in our faith to Him, just as Peter did.
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To add on what Annie said, there was also the example of the “woman who was a sinner” (7:36) who Jesus forgave, even though they were in presence of the Pharisees who strongly disagreed with his actions. There are so many examples that highlight Jesus’ forgiving nature.
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