In a medium saucepan, combine the chopped peaches, sugar, and 1 cup of water. Bring to a boil over medium heat, stirring occasionally until the peaches are soft and the sugar has dissolved, about 5-7 minutes.

Remove the saucepan from heat and let the peach mixture cool slightly. Once cooled, use a blender or immersion blender to puree the mixture until smooth.

Strain the peach puree through a fine mesh sieve into a large pitcher to remove any solids. Discard the solids.

Add the freshly squeezed lemon juice and 4 cups of cold water to the pitcher. Stir well to combine.

Taste the lemonade and adjust sweetness if desired by adding more sugar or water. Chill in the refrigerator for at least 30 minutes before serving.

Serve over ice cubes and garnish with fresh mint leaves if desired.