Why boil sugar for lemonade? I've started making home lemonade recently and all the recipes boil about one cup of sugar in one cup of water. I never questioned that until my father saw the process and asked why don't I just add water and sugar to lemon juice or add boiling water to the pitcher with lemon juice and sugar and I couldn't really tell, I just knew the sweetness was greater in my experience.
It's simply to allow the sugar to dissolve and mix into the lemonade.  Because of this, you can more precisely adjust your preferred sweetness level.