A cancer-stricken woman fighting a right-to-die battle against her parents won the backing of an appellate court Friday, which ruled that the 28-year-old bank manager from New York City who is paralyzed as a result of a brain tumor may decide her own fate. The emotional case has been playing out in Grace SungEun Lee’s room at North Shore University Hospital on Long Island, and on a Facebook page, Save Grace SungEun Lee, created by those who sided with family members desperate to keep Lee on life support. As word of the appellate court’s decision spread Friday, the page was swarmed with comments from people arguing for and against it, underscoring the passionate debate that surrounds the issue of individuals’ rights to choose death over terminal illness.