Yes and no. You can if you want. But you don't have to.
If you only need a little moisture, just put lip balm on your lower lip - and rub the lower and upper lip against each other so that the balm is massaged all over. In this way, you avoid getting shiny lips.
If you need a lot of moisture for your lips - and you like your lips to look moist/shiny - then put lip balm on your upper and lower lip and rub your lips together so that the lip balm is massaged all over.