~Apply vaseline/lip balm/papaw on your lips, and take a cotton bud (q-tip, whatever you wanna call it) and wipe it on your lips, rubbing it around to get rid of the dry skin. This is good for right before you do your base as when you come to your lips they will be moisturized and smooth. I've learnt that from Lisa Eldridge on You-tube.
~Something else you can do is make your own lip scrub, using olive oil & brown sugar or bicarbonate of soda. You can do this once a week to get rid of the dead skin.
Or you can indulge yourself & purchase a lip scrub by lush that comes in 3 flavours; bubblegum, (yum!) mint julip(choc-mint) & sweet lips (chocolate). Don't forget to apply lip balm after wards!