What is Aunt Alexandra's vision for what is "lady like"?

Aunt Alexandra represents the genteel South. While her brothers are easy going and laid back, as a woman, Aunt Alexandra doesn't have that luxury. She is stern and holds the values of the South in the highest regard. She tries to impart these in Atticus's children, though they challenge her more traditional ways.
When it comes to Scout, Aunt Alexandra's expects her to behave like a lady, not a child. When Scout wants to play with Walter, Aunt Alexandra prohibits it. She responds to Scout's request by saying, "I'll tell you why," she said. "Because—he—is—trash, that's why you can't play with him. I'll not have you around him, picking up his habits and learning Lord-knows-what."(23.86-87)
In addition to the value Aunt Alexandra places on lady-like, genteel behavior and her tacit disapproval of the way Atticus is raising his children, Aunty values the family name above all else. Scout's lady-like behavior, or her lack of it, affects the family name. We see this when she discusses other local families:
Aunt Alexandra, in underlining the moral of young Sam Merriweather's suicide, said it was caused by a morbid streak in the family. Let a sixteen-year-old girl giggle in the choir and Aunty would say, "It just goes to show you, all the Penfield women are flighty." Everybody in Maycomb, it seemed, had a Streak: a Drinking Streak, a Gambling Streak, a Mean Streak, a Funny Streak. (13.26)
Auntie's vision for what is lady-like, then, relies on the traditions of the past and on upholding the family honor.