Eh? Unless there's a specific priviso in the lease, usually any lawful activity can be undertaken by the retail tenant, including refusal of service to anyone, on private property. Not smart business-wise, but illegal?

The exception for race, color, ethnic background comes from the Civil Rights Act, but for some reason, while it includes restaurants, did not include retail stores, as part of businesses that could not discriminate on a racial basis. Unless I missed it, I don't think the Act has ever been broadened to include retail stores and Federal courts have routinely ruled against cases involving retailers.