Remove the kernel from the peaches and cut it into wedges. Combine water, sugar, lemon juice, and peaches in a blender. Blend until smooth and delicious.
freeze the granita
Pour the peach granita into a large baking sheet and place it in the freezer for 3 hours. Using a fork, scrape the granita every hour to eliminate any large frozen pieces. Repeat the process until the granita is frozen.
Divide the peach granita between six (cooled) glasses and serve immediately. Optionally sprinkle with fresh thyme leaves or lavender.