In a deep ceramic baking dish, combine the sliced peaches with granulated sugar, lemon juice, and cornstarch. Allow the mixture to sit for 10 minutes until a syrup starts to form.
In a separate bowl, mix together the oats, flour, brown sugar, and cinnamon. Cut in the cold butter using a pastry cutter until the mixture resembles large granulated brown sugar clusters.
Evenly distribute the crumble mixture over the peaches. Bake in a preheated oven at 375°F (190°C) for 40-45 minutes, or until the juices are bubbling at the edges and the topping is golden-brown.