Prepare mint simple syrup by combining 3/4 cup water and sugar in a small pot. Set pot over medium-high heat and bring to a boil. Stir until sugar dissolves and then remove from heat. Add mint and allow to steep until syrup has cooled. Strain and discard mint leaves. You should end up with a little over 1 cup of simple syrup.
While syrup is cooling, wash peaches, remove pits, and cut in chunks. Puree peach chunks in a blender or small food processor until smooth. Set a fine mesh sieve over a bowl and pour in peach puree, pushing it through using the back of a spoon. Discard skins/solids. You should end up with about 1 cup of peach puree.
In a pitcher, mix together 1 cup mint simple syrup, peach puree, fresh lemon juice, and remaining 2 cups water (store any leftover simple syrup in the fridge for another use). Refrigerate lemonade until chilled and/or serve over ice.
Feel free to adjust this recipe to your taste, adding more water, lemon juice or simple syrup.
This recipe can easily be halved or multiplied. Basically, you just need to use 1 part simple syrup, 1 part peach puree, 1 part lemon juice, and 2 parts water.
If possible, make sure that all of the components of your Peach Lemonade are chilled before combining them.