Fairness For Breastfeeding Mothers Act of 2019 (Sec. 2) This bill requires that certain public buildings that are open to the public and contain a public restroom provide a lactation room, other than a bathroom, that is hygienic and is available for use by members of the public to express milk. The lactation room must be shielded from public view, be free from intrusion, and contain a chair, a working surface, and (if the building is supplied with electricity) an electrical outlet. A public building may be excluded from such requirement at the discretion of the official responsible for its operation if it does not contain a lactation room for employees and does not have a space that could be repurposed as one or that could be made private by using portable materials, at a reasonable cost; or the cost of new construction required to create a lactation room is not feasible.