Apply a thick layer of gel paint remover across the brick to take off the previous coating of paint. Use a 4-inch-wide paintbrush to apply the gel and layer it on so it is at least 1/8 inch thick.
Leave the gel on for at least two hours. Check it periodically by using a scraper to lift part of the gel and see if the paint is peeling off under it. Peel off all the paint when it is ready. Reapply if necessary.
Wash the stripper residue off the walls with plain water and wait for it to dry thoroughly before proceeding.
Prime the masonry with either a sealer or primer specifically designed for use on a high alkaline surface. Look for a product that says it is for painting on high lime walls or masonry or that it is alkali-resistant. Use a 4-inch paintbrush to apply the primer and allow it to cure for the amount of time specified by the manufacturer before proceeding.
Paint the brick with 100-percent acrylic paint. The acrylic is more resistant to lime. Apply the paint as with the primer, using a 4-inch paintbrush and waiting until it is cured before using the wall. You can also apply a second coat for richer, longer lasting results.