Leprosy functions as a picture of uncleanness, like sin it meant you couldn't enter the temple, like sin it decimated your relationship with others. As Jesus heals this man we see his contagious cleanliness. If anyone else had touched the leper the uncleanness would have been contagious, it would have made them unclean, but not with Jesus. Jesus cleanses the man and then sends him to the priests to fulfil the law. To testify to his cleansing.
We don't know but I always wonder how the conversation between this and and the priests went, what exactly it was that the man testified too. Did he just make the offerings and they testified to his just being clean, or did his give testimony to the healing one who cleansed him. Action of the Messiah.
(15-16)As the scene closes Luke shows us that Jesus regularly withdraws to lonely places and pray. Jesus is concerned about his mission, he speaks regularly with his Father, he walks closely with him. Is it that he knows distraction is a danger? Or is there more to it. Luke doesn't tell us, except to record a number of times that Jesus follows this pattern. His relationship with his Father matters, he enjoys his sonship, a sonship he comes to proclaim and win for all.