Strengthening and Amplifying Vaccination Efforts to Locally Immunize all Veterans and Every Spouse Act or the SAVE LIVES Act This bill authorizes the Department of Veterans Affairs (VA) to furnish a COVID-19 (i.e., coronavirus disease 2019) vaccine to covered individuals during the COVID-19 public health emergency. Under the bill, covered individuals are veterans who are not eligible to enroll in the VA health care system; specified veterans who are eligible for hospital care, medical services, and nursing home care abroad; beneficiaries who are eligible for care due to a specified disability or death of a veteran; family caregivers of veterans who are participating in the VA's Program of Comprehensive Assistance for Family Caregivers; caregivers of veterans participating in the VA's Program of General Caregiver Support Services; caregivers of veterans participating in the VA's Medical Foster Home Program, Bowel and Bladder Program, Home Based Primary Care Program, or Veteran Directed Care Program; and the spouses of veterans. The VA must prioritize the vaccination of (1) veterans who are enrolled in the VA health care system, (2) veterans who fail to enroll but receive hospital care and medical services for specified disabilities in their first 12 months of separation from service, and (3) caregivers accompanying such prioritized veterans. Under the bill, the VA is authorized to offer a vaccine to the spouse of a veteran near the same time the veteran receives the vaccine.