I know two ways of making sure your lips stay soft and fairly smooth.
The first is to brush them using your toothbrush, at least once a day, after brushing your teeth. You don't have to rinse your brush before doing so. You can just incorporate it as part of your evening ritual to get rid of dead cells and leftover makeup.
The second is to use an old toothbrush. Put some petroleum jelly on your lips and let stay for at least thirty minutes. Then using your old brush, brush your lips to scrape off the dead skin cells that have been softened by the petroleum jelly. Wash your mouth after to get rid of the grease. Do this weekly.