On August 1, Amy Lam died less than 12 hours after giving birth. On Monday, on behalf of Ms. Lam's family, lawyers filed a notice of claim against the hospital, run by NYC Health & Hospitals, as well as more than a half-dozen doctors who treated Ms. Lam, alleging malpractice and medical negligence. NYC Health & Hospitals would not comment on the case because of pending litigation and patient privacy laws.