Melissa: I would say don’t. Facial scrubs may be too harsh for the lips’ thin skin. Some brands, especially the Japanese ones like Shiseido, don’t recommend scrubbing your lips. In fact, Shiseido doesn’t even have facial scrubs as they are deemed too aggressive. In its skincare regimes, sweeping cotton pads soaked in softener over the skin provide gentle exfoliation. In the same way, Shiseido’s Instant Eye & Lip Makeup Remover has exfoliating ingredients to lift away dead skin on your lips as you remove makeup.
If you really want to smoothen your puckers, try massaging lips gently with a damp soft-bristled tooth brush, or use an exfoliator made especially for lips. A DIY scrub I make: mix a teaspoon of honey with brown sugar and rub on lips, then rinse. Remember to slick on a lip treatment or a lip balm after to protect and hydrate.