Add sugar to a gallon pitcher and pour hot water over sugar, stirring to dissolve. Add strawberries to a blender or food processor and puree. Add the strawberry puree, fresh lemon juice, and cold water to the pitcher. Stir until well-combined. Refrigerate until ready to serve. When ready to serve, add ice, fresh lemon slices, fresh strawberry slices, and/ or mint, if desired. Keep refrigerated.
Strawberry lemonade will keep in the refrigerator for up to 3 days without the fresh fruit or mint added to the liquid. Kid-Friendly Version:If your children do not enjoy the pulp of strawberries, strain the strawberry puree through a fine mesh strainer before adding to the pitcher.