Sand the entire surface of the new- and old-textured walls using a sanding buffer with a medium-grain sanding ring. Go over the areas with more texture more than areas with less texture. This evens out the walls and smooths down any areas that are chipped or peeling.
Vacuum the walls and surrounding areas using a shop vacuum. This gets rid of dust and debris caused by sanding.
Cover the end of a flat-ended trowel with plaster spackle, then hold the trowel against the wall at a 45-degree angle. Slide the trowel against the wall, maintaining the angle, while keeping the trowel approximately a quarter-inch above the wall. This motion helps apply the spackle in a textured, choppy way that resembles stone.
Repeat to cover all of the walls with the same amount and thickness of spackle. Allow the plaster spackle to dry for 8 to 12 hours.
Fill a paint tray with latex wall paint, then coat a paint roller in the paint.
Apply the latex paint over the newly textured walls using the paint roller. Allow the paint to dry for 8 to 12 hours.