What hard lesson does Jem learn from Mrs. Dubose's medical problem?

In Chapter 11, Atticus punishes Jem for destroying Mrs. Dubose's camellia bush and makes him read to her ever day for two hours, except for Sundays, for an entire month. Later on in the chapter, Mrs. Dubose passes away, and Atticus explains to his children that Mrs. Dubose suffered from a chronic disease and was addicted to morphine. Atticus tells Jem that his reading occupied Mrs. Dubose's mind and helped her beat her morphine addiction. Atticus then tells his children that he wanted them to see what real courage looked like. Atticus says,

"I wanted you to see what real courage is, instead of getting that idea that courage is a man with a gun in his hand. It's when you know you're licked before you begin but you begin anyway and you see it through no matter what" (Lee 69).

Jem learns an important lesson about "real courage." According to Atticus, Mrs. Dubose was the bravest person he's ever met for conquering her morphine addiction. Jem learns that Mrs. Dubose was courageous and had a strong will. He realizes that Mrs. Dubose's will to conquer her extremely painful illness demonstrated her integrity and courage.