Lessening Regulatory Costs and Establishing a Federal Regulatory Budget Act of 2021 This bill establishes procedures and provides statutory authority to reduce the number of federal regulations. Specifically, it requires each agency to establish a regulatory reform task force chaired by a designated regulatory reform officer. Each task force must, among other duties (1) review each existing agency regulation; (2) estimate the potential cost savings of repealing or modifying each regulation; and (3) identify regulations that are appropriate for repeal, replacement, or modification based on cost, effectiveness, and impact on employment. The bill further provides statutory authority for the executive order prohibiting agencies from issuing a new regulation with an economic impact of at least $100 million without identifying two regulations for repeal that will offset the cost of the proposed new regulation. Agencies also must submit a list of all planned regulatory actions for inclusion in the semiannual Unified Agenda of Federal Regulatory and Deregulatory Actions, including (1) the estimated economic effect of each action, and (2) proposed deregulatory actions to offset the cost of each proposed new regulation. Additionally, the Office of Management and Budget must establish an annual regulatory budget for each federal agency that specifies the net allowable increase in regulatory costs for each agency during the next fiscal year.