In a blender, combine the sliced peaches and 1 cup of cold water. Blend until smooth.
Strain the peach puree through a fine mesh sieve into a large pitcher, pressing down with a spatula to extract as much juice as possible.
Add the granulated sugar to the peach juice and stir until dissolved.
Pour in the freshly squeezed lemon juice and the remaining 3 cups of cold water. Mix well.
Taste the lemonade and adjust sweetness by adding more sugar if desired.
Chill the peach lemonade in the refrigerator for at least 1 hour before serving.
Serve over ice and garnish with lemon slices, peach slices, and fresh mint leaves if desired.