Thoroughly wash your lemons in cold water. Roll each lemon firmly against your countertop using the palm of your hand to release the juices before cutting. Cut the lemons in half and squeeze to extract 1 cup of fresh lemon juice. Zest one lemon before juicing.
Combine sugar and 1/2 cup of water in a small saucepan. Heat over medium heat until the sugar completely dissolves (approximately 3 minutes), stirring occasionally. Remove from heat and let cool completely.
In a high-powered blender, combine the frozen peach slices, lemon juice, cooled simple syrup, and 1 cup of cold water. Blend on high for 60 seconds or until the mixture becomes smooth.
Add the ice cubes and remaining water to the blender. Pulse several times to break down the ice, then blend on high for another 60-90 seconds until you achieve a slushy consistency.
Taste your frozen peach lemonade and adjust sweetness or tartness as needed. For a thicker consistency, add additional ice; for a thinner drink, add more cold water.
Pour into glasses, garnish with fresh mint leaves and serve immediately.