Add water to a medium pot and bring to a low boil. Add the peaches. Cook for 2 minutes. Remove from the heat, drain, and transfer to a bowl of ice water. Peel the skins from the peaches, remove the pit, and cut into fourths. Add the peaches to a food processor or blender and puree until smooth. Transfer to a bowl and set aside.

Combine the water and sugar in a medium pot and bring to a boil until the sugar dissolves. Stir in the puree and lemon juice. Remove from the heat and carefully transfer the mixture to a medium bowl. Cover and chill in the refrigerator until cool.

Transfer the bowl to a freezer and freeze the mixture for 3-4 hours. Remove the bowl from the freezer and gently mix with a fork. Return the bowl to the freezer.

When you are ready to serve, let the granita slightly soften and then gently stir in the strawberries. Scoop into individual glasses or serving bowls with a spoon. Garnish with mint over the top, if desired. Serve immediately.