Lower Costs, More Cures Act of 2021 This bill establishes and modifies several programs and requirements to address prescription drug prices. The bill modifies provisions under Medicare and Medicaid relating to prescription drug coverage and price transparency. 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; requires pass-through pricing models, and prohibits spread-pricing, for payment arrangements with PBMs under Medicaid; and allows states to include in the Medicaid Drug Rebate Program covered outpatient drugs that are provided as part of physician or outpatient hospital services. The bill also generally modifies other provisions relating to the regulation and costs of generic and brand-name drugs. Among other changes, the bill prohibits the manufacturer of a brand-name, generic, or biosimilar drug from entering into certain agreements to resolve or settle a patent infringement claim in connection with the sale of a drug or biological product; permanently allows high deductible health plans to waive deductibles for insulin and associated products; and establishes the position of Chief Pharmaceutical Negotiator in the Office of the U.S. Trade Representative.