First of all, while I am not at all certain as to what the "huswife" is that Miss Steele refers to, I assumed it to be the needlebook that was given to her and Lucy by Fanny earlier.

As to Lucy's continuing the engagement, I can only presume that she still has some hope that Edward's mother might relent a little, and give them more than the nothing that Edward is currently inheriting. Also, she has no other hopes of catching anyone else any more wealthy at present. Edward is still a decent catch, and with her background, she is still quite lucky. She is not as young as she once was either, and "making another conquest" might prove more difficult for her now. But I suppose the only people who can really answer this question are Jane Austen and Lucy Steele herself. ;-)