You would think it would be pretty strange that Atticus would say this about Mrs. Dubose. After all, she pretty much stands for everything he hates. She is so horribly racist and she is willing to abuse Atticus's own family because of his stands on racial and other issues.
But Atticus admires her anyway because of the way she fights off her morphine addiction in the month or so before she dies. He respects her determination and her bravery. This is why he says she is a great lady. He says that courage is the determination to get back up again even though you know you're "licked."
The Reader might think that Atticus would not like Mrs. Dubose let alone call her a “great lady” when he says ‘“She has her own view about things, a lot different from mine…”’ (Lee 112). Atticus views Mrs. Dubose as a “great lady” not for her ideas or views, but because she is determined and brave. Atticus thinks this way of Mrs. Dubose because when she is dying she talks to Atticus about writing her will. When they were done Atticus told Jem that Mrs. Dubose said “‘… she was going to leave this world beholden to nothing and nobody”’ (Lee 111). Mrs. Dubose was a morphine addict and she wanted to break away from the drug, which she did. When she died Atticus said ‘“As the mountain air”’ (Lee 111). Meaning she was free from Morphine. This act of hers made Atticus believe she was determined and the bravest person he had ever met.
she is great lady to him because she was a nice person when he was a boy.