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When Elizabeth visits Charlotte and Mr. Collins, she becomes part of Lady Catherine's society. Lady Catherine asks Elizabeth a lot of personal questions. Elizabeth succeeds in dodging some, and handles Lady Catherine's authoritative attitude with good grace.
With her nephews in town, Lady Catherine is bored with the Collinses and Elizabeth but dutifully invites them over anyway. She comments on Elizabeth's piano playing, suggesting ways for Elizabeth to improve.
When she hears rumors that Elizabeth and Darcy are engaged, Lady Catherine drives down to Longbourn to try to find out if it's true. She informs Elizabeth that Mr. Darcy and her daughter are meant to be together, and unsuccessfully tries to induce Elizabeth to promise that she will not become engaged to Mr. Darcy.
After her failure with Elizabeth, Lady Catherine goes straight to London, where she tells the story to Mr. Darcy, hoping that he will be horrified at Elizabeth's impertinence. Unfortunately for her, she gives Mr. Darcy hope. He realizes that, if Elizabeth did not care for him at all, she would have let Lady Catherine know that straightaway. So, indirectly, Lady Catherine is the reason Elizabeth and Darcy at last get together.