Lethal Means Safety Training Act This bill requires the Department of Veterans Affairs (VA) to update its Lethal Means Safety and Suicide Prevention training course at least once a year to ensure it is culturally appropriate and uses best practices identified by subject matter experts (e.g., veterans service organizations). The bill requires certain VA employees and care providers to take the most recently updated version of the training course within 90 days after the person is hired, agrees to furnish care, or receives support and at least annually thereafter. Specifically, the bill requires the following categories of VA employees or care providers to take the training course: employees of the Veterans Health Administration or Veterans Benefits Administration who regularly interact with veterans, compensation and pension examiners, employees of Vet Centers or vocational rehabilitation facilities, employees of Veterans Community Care Providers who provide care to veterans, and caregivers receiving support under the Program of Comprehensive Assistance for Family Caregivers or the Program of General Caregiver Support Services. The VA must publish the training course on a publicly available VA website. Additionally, the VA must publish a report on its website that includes the percentage of individuals in each category who have completed such training.