Make the simple syrup: Combine sugar with 1 cup of water in a small saucepan. Heat over medium heat, stirring occasionally until sugar completely dissolves (about 3-5 minutes). Remove from heat and let cool completely.
Prepare the lemons: Roll lemons on the counter with firm pressure to help release juices. Cut in half and juice them until you have 1 cup of fresh lemon juice. Strain out seeds and pulp.
Process the peaches: Place peach slices in a blender and pulse until smooth. Pour through a fine-mesh strainer into a bowl, pressing with a spoon to extract all the juice and discard solids.
Process the raspberries: Repeat the same process with raspberries, blending until smooth and then straining to remove seeds.
Combine the base: In a large pitcher, combine the lemon juice, strained peach puree, and about ¾ of the raspberry puree (reserve some for layering effects).
Add remaining ingredients: Pour in the cooled simple syrup and remaining 3 cups of cold water. Stir well to combine.
Create the gradient effect (optional): For a beautiful layered look, add ice to glasses, pour lemonade about ¾ full, then gently pour a small amount of the reserved raspberry puree on top. It will slowly sink, creating a beautiful ombre effect.
Serve and garnish: Add ice to each glass, garnish with fresh mint leaves and fruit slices if desired, and serve immediately.