Make the simple syrup: In a small saucepan, combine 1 cup of sugar and 1 cup of water. Bring to a boil and stir until the sugar has dissolved completely. Remove from heat and let it cool for about 30 minutes.

Juice the lemons: While the syrup is cooling, juice the lemons to make 1 cup of lemon juice. Strain the juice to remove seeds and excess pulp for a smoother lemonade.

Combine and mix: In a large pitcher, combine the cooled syrup, lemon juice, and 4 cups of cold water. Stir well.

Adjust flavor as needed: Taste your lemonade and adjust the sweetness or tartness by adding more sugar, lemon juice, or water according to your preference.

Chill and serve: Add ice cubes directly to the pitcher or to individual glasses. Garnish with lemon slices and mint leaves if desired. Serve chilled.