Lummis-Gillibrand Responsible Financial Innovation Act This bill provides for the regulation of crypto assets. The bill outlines agency jurisdictions over types of crypto assets and ancillary assets. For example, the bill provides that the Commodity Futures Trading Commission (CFTC) has jurisdiction over crypto assets that do not provide their holders with financial interest in a business entity. The bill also establishes consumer protections, including by requiring (1) a crypto asset intermediary to provide proof of possession or control of all its crypto assets, and (2) an annual verification of assets by an independent public accountant. The bill also provides for the establishment of customer protection and market integrity authorities upon approval by the Securities and Exchange Commission (SEC) and the CFTC. In addition, the bill imposes criminal penalties for violations of certain financial recordkeeping requirements involving crypto asset transactions. Further, the Department of the Treasury, the SEC, and the CFTC must assess the compliance of the entities they regulate with anti-money laundering programs and countering the financing of terrorism requirements. Under the bill, any stablecoin must be issued by depository institutions. Institutions must hold 100% of the value of all outstanding stablecoins in reserves and allow stablecoins to be redeemed at par. The bill also provides for the tax treatment of crypto assets, including an exemption from income tax for purchases using digital assets that result in a gain or loss of $200 or less.