Medical Laboratory Personnel Shortage Relief Act of 2024 This bill adds medical laboratory professionals to the National Health Service Corps (NHSC) and establishes a grant program to fund education programs for medical laboratory professionals. Specifically, it makes medical laboratory professionals eligible to participate in the NHSC, which provides scholarships and student loan repayment awards to health care providers who agree to work in areas with health care provider shortages. The bill also authorizes the Department of Health and Human Services to award grants to, or enter into contracts with, certain hospitals, schools, and nonprofits to develop and operate accredited education programs that award degrees or certificates to medical laboratory professionals.