Living Donor Protection Act of 2019 This bill prohibits discrimination based on an individual's status as a living organ donor in the offering, issuance, cancellation, coverage, price, or any other condition of a life-insurance policy, disability-insurance policy, or long-term-care insurance policy. The bill also specifically includes recovery from organ-donation surgery as a serious health condition that entitles covered private-sector and federal civil-service employees to medical leave. The Department of Health and Human Services must update public-service announcements, websites, and other media regarding live organ donation to educate the public on the benefits of live organ donation and on access to insurance for living organ donors.