Combine the sugar with 1 cup water in a medium saucepan and bring to a boil. Reduce heat and allow the sugar to dissolve, 3 to 4 minutes. Remove from heat and cool completely.
Combine the lemon juice, sugar syrup, and 4 cups cold water in a large pitcher. Refrigerate until well chilled, at least 1 hour. Serve over crushed ice and garnish with mint leaves and sliced lemons.
For a twist on classic lemonade, try infusing the sugar syrup with fresh basil, a scraped vanilla bean or freshly grated ginger root. Add it to the syrup while it cools. Strain out any solids before using.