The correct option is A She has found something to write about.
"Lady Bertram's hour of good luck came." - this sentence specifically implies that Lady Bertram had finally found something to write about. It is also evident that Lady Bertram finally found something to write about because her niece, Fanny, received a letter from her. So, option A is the best answer. B is not correct because we do not know the subject of her letter. C and E cannot be the answer because they do not fit the context of the question, and option D is irrelevant to the context.