Preheat the oven to 375°F (190°C). In a large bowl, gently toss sliced peaches with granulated sugar and lemon juice until evenly coated.
Transfer the coated peaches into a 9-inch baking dish, spreading them out into an even layer.
In a separate mixing bowl, combine oats, flour, brown sugar, and cinnamon. Mix thoroughly to blend all dry ingredients.
Add the cold, diced butter to the dry mixture. Using a pastry cutter or fork, cut the butter into the mixture until it resembles coarse crumbs with some pea-sized pieces.
Sprinkle the crumble topping evenly over the peaches in the baking dish, covering all the fruit.
Place the dish into the oven and bake for about 40 minutes, or until the topping is golden brown and the filling is bubbling around the edges.
Remove from the oven and let it cool slightly. The crumble should be fragrant with a crisp topping and tender, juicy peaches underneath.