Strain the lemon juice into a large serving container or pitcher, removing the seeds and pith. Stir in the sugar until dissolved.
Add 4 cups cold water and continue stirring until well combined. Add the lemon slices. Just before serving, add ice into cups and pour 1 cup lemonade into each. Stir or swirl 1/2 to 3/4 cup pink cotton candy into each glass of lemonade until dissolved.