I find it really interesting that you are asking about the character of Luke in this coming-of-age story! The reason is because it is Matt and the narrator, Kate, who are usually the focus. Matt forgoes the world of academia in order to marry a pregnant Ms. Pye. Kate is the youngest child at the death of their parents and ends up being the only one to pursue a college career. She originally judges her siblings and, by the end, sees the error of her ways. Luke, though, psychologically becomes the father-figure of the family and cognitively moves from academia into the working world.
First, let's explore Luke psychologically in Crow Lake. At 19, both of Luke's parents have died tragically. Luke's parents' dream was for all of their children to go to college. At first, Luke intends to follow that plan and attend the teachers college, but then he realizes that he must take care of the family instead. Psychologically, Luke has to become the father of the family now, as the oldest child is often asked to do. The role fits Luke well. He is not overly academic, like Matt is. Of course, this switcheroo causes tension between the two siblings. Luke works as much as he can for his neighbors, the Pyes. This decision allows for the eventual academic success of Kate and the eventual working success of Matt. Even though this change is different, it is beautiful. As Kate says later in the novel:
It is approach that is important--the openness, the ability to see, without being blinded by preconceptions.
Luke also changes his career plan in regard to cognition. It takes a high level of thought to go into academics. Even though Luke was slated to this track according to his parents' will, that is not the eventual track he chooses. Luke realizes that he is not as academically minded as Matt and, therefore, gives up his spot so Matt can pursue his dreams eventually. Luke's job, as the psychological patriarch, is to keep the family together. Even though the two brothers fight because of Luke's decision, the family DOES stay together.
Luke's change reminds me a lot of the differences between college prep and career prep in high school. Luke is forced to mature psychologically as a result of being the patriarch of the family before his time.