This question is a subjective one because each person's perspective will shape what they find to be "most important." I've read this novel multiple times teaching it to ninth-grade classes, and the most important thing we, as a group, seem to notice is how Junior learns to trust himself and forge his own path.

At the beginning of the novel, Junior tells the reader about all of the physical and social issues he has had to overcome at such a young age. He makes it clear he does not fit in with anyone except his grandmother, Eugene, and Rowdy. These trials and tribulations cause Junior to want more from his life. He makes a difficult choice to leave the Rez and try for a better education at Reardon, a white school over 20 miles away. This choice causes him to suffer even more problems than before.

However, this choice changes his life for the better, and it gives Junior the strength to keep making choices that benefit himself and his future. By the end of the novel, he finds that sticking to his guns and following his own life path brings him to a place of acceptance. Yes, he has faced significant hardship and trauma, but Junior realizes all of those experiences are a part of life. He also learns that he wants more than what the Rez has to offer. By believing in himself and not following the crowd, Junior learns he has a world of possibilities for him to choose from. He can succeed and create a better future for himself by simply being himself.

The most important lesson Junior learns in The Absolutely True Diary of a Part-Time Indian is that it's all right to be who he is, a "part-time Indian" split between a largely white world of wealth, privilege, and hope, and a reservation world of poverty, racism, and despair. Junior battles external and internal pressures throughout the novel. His white high-school classmates inflict racist insults on him ("Indians are living proof that niggers fuck buffalo," one tells him) or generally cast him as a loser, while his peers on the reservation see him as a traitor. Internally, he alternates between guilt, shame, and pride as he navigates his disparate experiences. Eventually, he figures out that he is embracing elements of his nomadic heritage. It is OK to embrace tradition, and it also acceptable to embrace the hope represented by the white person's world, and to leave the reservation.

I realized that, sure, I was a Spokane Indian. I belonged to that tribe. But I also belonged to the tribe of American immigrants. And to the tribe of basketball players. And to the tribe of bookworms. And the tribe of cartoonists. And the tribe of chronic masturbators. And the tribe of teenage boys. And the tribe of small-town kids. And the tribe of Pacific Northwesterners. And the tribe of tortilla chips-and-salsa lovers. And the tribe of poverty. And the tribe of funeral-goers. And the tribe of beloved sons. And the tribe of boys who really missed their best friends. It was a huge realization. And that's when I knew that I was going to be okay.

Junior learns many other lessons in the book, but this one—the discovery of who he is, and that there's nothing wrong with being the way he is—comforts his soul, emotionally equipping him to meet practical challenges.

I agree with the above post.  Off the back of the idea about "singular conceptions of good," Junior learns that the face of friendship is not always one of laughter and good times.  For the majority of the novel, he and Rowdy are at odds because Rowdy feels like Junior is a traitor.  Junior tries to regain Rowdy's friendship and does not really understand the complicated feelings that Rowdy has over Junior's going to Reardan.  At the end of the novel, the two boys play basketball "without keeping score" which symbolizes the growth that their relationship has had--they no longer let the element of competition stand between them.  Junior learns that a friendship may grow through struggle and conflict.

As with any question of this nature, there will be considerable debate.  I think that embracing the divergence of thought will allow a better answer or discussion to emerge.  In my mind, I would say that Junior's most important lesson is that human consciousness is fluid enough to embrace different conceptions of self.  Junior is poised between two competing communities in terms of the Native American community into which he is born and the White one in which he goes to school.  Through  the different experiences the Junior has in both worlds, he understands that human beings are more than singular conceptions of the good.  His father might be lacking in being a source of support for Junior, but he does care for him.  The reservation might be a source of pain, but it is a part of Junior's identity and cannot be negated.  Junior is a Spokane Indian, but he is also an athlete, an artist, a thinker, and someone who is able to wear different hats in constructing his own identity.

What is the most important lesson that Junior learns during the course of The Absolutely True Diary of a Part-time Indian?

In The Absolutely True Diary of a Part-time Indian, the protagonist Junior (Arnold Spirit) learns that his identity is worth fighting for.  Throughout the novel, Junior has to battle with "monsters" who stand in his way:  poverty and alchoholism on the Spokane Indian reservation, poor education, the abuse of his best friend Rowdy, the death of loved ones, racism at Reardan.  Although Junior's life would in some ways be much easier if he assimilated into the lifestyle of his environment, he decides to instead take a different road to find himself and his own happiness.  Junior cannot accept the poor education offered to him on the reservation, so he decides to attend school at Reardan.  From here, all becomes complicated, but Junior toughs out all the trials that are thrown his way.  In the end, he and Rowdy become friends again, and Junior learns to love the good aspects of the reservation.  So in the end, Junior puts himself on a path to continue to explore and develop his identity.