Prepare Peaches: Chop peaches, removing pits but leaving the skin on.
Cook Mixture: In a medium saucepan, combine peaches, 2 cups of water, and sugar. Bring to a boil, then reduce heat and simmer for 5–7 minutes, until peaches are soft and mushy.
Cool: Remove from heat and let cool for about 10 minutes. Transfer to the refrigerator until fully chilled.
Strain: Strain the peach mixture through a fine mesh sieve to remove pulp, pressing to extract as much liquid as possible.
Mix: Stir in the remaining 2 cups of cold water and the fresh lemon juice.
Serve: Pour over ice and garnish with fresh mint and peach slices if desired.