I think if you use lemon juice, you should apply it with glycerine or honey. I searched for recipes which include either glycerine or honey. So pick one of those.
Here is a recipe to mix up and apply before bedtime. Because of the lemon, refrigerate leftovers for future use.
½ teaspoon vegetable glycerine (or honey)
½ teaspoon fresh lemon juice
The glycerine brings moisture into your lips while the lemon juice exfoliates, removing dead skin cells. Honey contains Sugar crystals that exfoliate the skin of the lips and the honey itself hydrates lips.