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

Remove the saucepan from heat and let the peach mixture cool for about 10 minutes.

Once cooled, blend the peach mixture in a blender until smooth. Strain the puree through a fine-mesh sieve into a large pitcher to remove the pulp, pressing down with a spatula to extract as much liquid as possible.

Add the fresh 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 and garnish with fresh peach slices and lemon wedges if desired.