The centurion in Luke chapter 7 sends people to Jesus so that he will heal a sick slave of his.  And when Jesus is almost to the centurion, the centurion sends friends to tell Jesus that he is not worthy of this service.  But rather than listening to them Jesus says “not even in Israel have I found such faith”.  Here Luke’s gospel is depicting Jesus as appealing to more people than just the Jews, and therefore it is important to show that the gentiles have just as much or more faith than the Jews.  Since gentiles are getting the word even as easily or easier than Jews it makes the story seem more inclusive to them.  This is similar to what Peter tells to the centurion from Caesarea in Acts chapter 10.  Peter tells him that “God shows no partiality, but in every nation anyone who fears him, and does what is right is acceptable to him” (Acts 10:34-35).  Once again saying that Jesus is interested in everyone.

Jesus tries to reach out to Samaria as well, although in chapter 10 of Luke Jesus and the disciples are not greeted well, which even leads James and John to ask Jesus if they should command fire down from heaven on the people.  Although Jesus does not send down fire on them, he does rebuke them, before leaving.  While this event did not go well, it did depict Jesus trying to spread the word to the Samaritans who were not popular among the Jews.  A slightly more successful narrative is in Luke chapter 17 where Jesus is going from Samaria to Galilee and he heals 10 Lepers, of which only one returns to thank him, in the narrative the one who happens to come back to thank Jesus is a Samaritan.  Luke is continuing the theme of Jesus as the savior to everyone by having him heal a Samaritan. Not only does Jesus heal him, since he comes back to thank Jesus it makes the samaritan seem more righteous than the other ones who did not bother to thank Jesus.  
Luke wants to show that Jesus is being fair minded to everyone including the Samaritans, and when a Lawyer asks Jesus what he should do to inherit eternal life.  Jesus asks him what the law says, and the lawyer replies that “You shall Love the Lord your God with all your heart, and with all your soul, and with all your strength, and with all your mind” (Lk 10:27).  But the lawyer then asks who he should consider as his neighbor, then Jesus gives an example of a man getting beaten by robbers, and then only a Samaritan would help him.  Which is depicting Jesus as considering everyone your neighbor.  Then before Jesus leaves earth he says “…you will be my witnesses in Jerusalem, in all Judea, and Samaria, and to the ends of the earth” (Acts 1:8).  This was Jesus’ instructions to the disciples right before being taken up by a cloud.  Luke is trying to say that the followers of Jesus need to continue teaching about Jesus to the far reaches of the earth at the time, which for them was Rome.