Local Food Assistance and Resilient Markets Act of 2020 or the Local FARM Act of 2020 This bill addresses provisions related to programs of the Department of Agriculture (USDA), including the Specialty Block Grant Program, the Supplemental Nutrition Assistance Program (SNAP, formerly known as the food stamp program), the Loan Agriculture Market Program, and the Farm Microloan Program. USDA must provide grants to states under the Specialty Block Grant Program to procure and distribute specialty crops to needy persons at zero cost to those persons. Each grant distributed shall not exceed $2.5 million. The Food and Nutrition Service of USDA must distribute grants to state agencies to develop tools and provide technical assistance to (1) increase the quantity of retailers that accept and redeem SNAP benefits online, and (2) expand the capacity of retailers to accept and redeem SNAP benefits online. The bill temporarily reduces the matching funds requirement for certain nutrition programs under the Local Agriculture Market Program. Additionally, the bill expands funding under such program to include (1) providing grants to organizations that serve socially disadvantaged farmers or ranchers, and (2) making payments to certain entities for COVID-19-related losses. The bill also extends the Farm Microloan Program and temporarily waives certain eligibility requirements for the program during the COVID-19 public health emergency.