What valuable lessons did Roger learn from Mrs. Luella Bates Washington Jones?

The lesson of compassion is one of the most important lessons that Roger learns from Mrs. Jones.

To be compassionate means to show sympathy towards another person.  Mrs. Jones shows tremendous compassion towards Roger.  When she catches him as he tries to steal her purse, she could have turned him over to the police. She could have abused him for what he did.  However, she displays a tremendous amount of compassion in taking him home, feeding him, cleaning him up, and teaching him that he should not steal from others. Finally, she gives him the money that compelled him to steal in the first place.  At the end of the story, Roger stands in the hallway and it is clear that he has learned the lesson of grace and compassion from Mrs. Jones.  While we don't know what will become of him, it's logical to presume that she has impressed upon him how important it is to treat human beings with compassion.

Roger has learned the lesson of seeing people as more than they appear to be.  Initially, Roger saw Mrs. Jones as a target for a robbery.  However, when she takes him in, he sees her as something more. He volunteers to go to the store for her, eats her food, and listens to her story.  When she says to him, “I have done things, too, which I would not tell you, son—neither tell God, if he didn’t already know," it has an effect on Roger. As a result, Roger wants to earn her trust:

But the boy took care to sit on the far side of the room where he thought she could easily see him out of the corner of her eye, if she wanted to. He did not trust the woman not to trust him. And he did not want to be mistrusted now.

Roger has learned the lesson of seeing people as more than they appear to be.  Every person has a story and this allows them to connect to other people. Roger has learned this lesson in the way he wants to be seen by Mrs. Jones after he gets to know her.