In what ways was Isabel lucky? In what ways was she unlucky? How did she try to control her fate and change her luck?

I'm not sure how she is lucky. Things don't go well for her. Isabel and Ruth are slaves. After being sold after the death of her beloved mistress, the girls suffer from all kinds of abuse at the hands of their new owners, the Locktons. Through it all, Isabel makes her and her sister's safety her top priority, working with the patriots as a spy among her British-sympathizing masters in exchange for the promise of freedom. She persists in her goal of freedom despite her sister being sold, being loaned out to a new mistress, a fire which consumes most of NYC, and repeated failures in her espionage work. You might consider that throughout her story, Isabel gradually learns the value of kindness as she is repaid dearly by the people whom she treats well.