In a blender, combine the peaches, strawberries, and ½ cup of water. Blend until smooth.
Pour the blended mixture through a fine mesh sieve into a large pitcher to remove any pulp, pressing gently with a spoon.
Add the lemon juice and sugar (or honey) to the pitcher. Stir until the sugar dissolves completely.
Stir in the remaining cold water. Adjust sweetness or tanginess by adding more sugar or lemon juice, as needed.
Fill glasses with ice cubes and pour the lemonade over. Garnish with fresh mint leaves if desired.