It seems that Austen is portraying Lady Catherine in a satirical way--mocking the pompous, snobby aristocratic ladies of her day. It is ironic that Catherine is the sole, independent female in the whole story as she is truly the most despicable woman in the book.
Austen provides us with great insight into Lady Catherine's character. Lady Catherine invites her rather servile visitors to supper at her rich mansion, but then proceeds to lead every conversation, seeming to think that she knows absolutely everything and all who surround her are idiots:
"...delivering her opinion on every subject in so decisive a manner, as proved that she was not used to have her judgement controverted. She inquired into Charlotte's domestic concerns familiarly and minutely, gave her a great deal of advice as to the management of them all; told her how everything ought to be regulated in so small a family as hers, and instructed her as to the care of her cows and her poultry. Elizabeth found that nothing was beneath this great lady's attention, which could furnish her with an occasion of dictating to others" (Chapter 29).
To top off her ego, Lady Catherine befriends the "lowly" (such as Mr. Collins, who is too easily overawed) that she may be worshiped as the social and intellectual leader in all things. I believe Elizabeth Bennet's appearance is quite an affront to her. Lizzy penetrates her character in an instant, and replies with sharp repartee to Lady Catherine's astoundingly invasive personal questions. The event is a perfect storm of wit and arrogance.
It is no surprise to see her show up at the Bennet household once she catches wind of her nephew's proposal. She fears losing the control she thought she had over the family; mostly, I believe, she fears her daughter will lose the match that Lady Catherine had "decided" on already.