Some earlier posts suggested that Anne is coming into her own in Lyme because she is achieving some kind of closure over her relationship with FW: accepting that she won't ever marry him, etc. I also feel that Lyme and its immediate aftermath represent a turning point, but not in quite the same way: although Anne is flattered by the interest of Captain Benwick and later Mr. Elliot, I think it's pretty clear (even before Louisa takes herself out of the game) that FW is still what Anne wants.

I think our sense that Anne is coming into her own actually has less to do with FW than with his friends, and the world they represent: it's in Lyme that Anne recognizes that she has moved beyond the limited world she grew up in and the values it represents. Her first reaction on meeting Benwick and the Harvilles and seeing the frankness and affection in their relationships is "These would have been all my friends," and it is that thought, not her grief over FW, that forces her "to struggle against a great tendency to lowness" (ch. 11) -- this could have been her world. Back with Lady Russell after the accident, Anne finds that, unlike LR, she's no longer terribly interested in the doings of her own family: "how much more interesting to her was the home and the friendship of the Harvilles and Captain Benwick." (ch. 13). Later in the same chapter, for the first time, Anne acknowledges to herself that Kellynch and its tenants are better off with the Crofts than with her own relatives; and soon we learn that "Admiral Croft's manners were not quite of the tone to suit Lady Russell, but they delighted Anne."