Lower Costs, More Cures Act of 2021 This bill establishes and modifies several programs and requirements to address prescription drug prices, particularly in relation to Medicare and Medicaid. Among other changes, the bill requires the Centers for Medicare & Medicaid Services to publish certain information, as reported by pharmacy benefit managers (PBMs), relating to generic dispensing rates, drug discounts and rebates, and payments between PBMs, health plans, and pharmacies; caps annual out-of-pocket spending under the Medicare prescription drug benefit; allows prescription drug plan sponsors under the Medicare prescription drug benefit to offer additional plans in a region; establishes requirements under the Medicaid Drug Rebate Program for certain gene therapies for which prices are indexed to achieved outcomes; and establishes the position of Chief Pharmaceutical Negotiator in the Office of the U.S. Trade Representative.