Lifelong Learning and Training Account Act of 2021 This bill establishes tax-exempt savings accounts that may be used to pay for training expenses and will be managed by state programs known as Lifelong Learning and Training Account programs. Tax-exempt distributions from an account may be used for training that results in a recognized postsecondary credential, such as an industry-recognized certificate or certification, a license recognized by the federal government or a state, or an associate or baccalaureate degree. The bill specifies contribution limits, age restrictions, and income limits that apply to beneficiaries of the accounts. Accounts that meet the requirements are eligible to receive certain federal matching funds for contributions made by the beneficiary or an employer.