Add the frozen peaches, water, and granulated sugar to a small saucepan and bring to a simmer. Simmer for 10 minutes then remove from heat and allow to cool to room temperature.
After cooling, pour the syrup through a fine-mesh sieve to separate out the peaches.
Add the water, lemon juice, and ¾ cup of the peach simple syrup to a medium pitcher with ice. Stir together and serve chilled.
Notes
The simple syrup recipe yields just about 1⅓ cups of simple syrup total. Feel free to add more to the lemonade to reach desired sweetness. Leftover simple syrup can be stored in a sealed bottle in the refrigerator for up to 1 week.
Store the lemonade in the refrigerator, covered, for up to 5 days.