Preheat your oven to 375°F (190°C). In a large bowl, toss sliced peaches with sugar and lemon juice until well coated. Spread the peaches evenly in the prepared baking dish.
In a separate mixing bowl, combine flour, oats, brown sugar, and cinnamon. Stir to mix evenly.
Add the cold butter cubes to the dry mixture. Use a pastry cutter or fork to cut the butter into the mixture until it resembles coarse crumbs with some pea-sized pieces.
Spoon the crumble mixture evenly over the peaches, covering the fruit completely. Gentle pressing is okay to ensure even coverage.
Place the baking dish in the preheated oven and bake for about 35 minutes, or until the topping is golden brown and bubbling around the edges.
Remove the crumble from the oven and let it cool slightly for about 10 minutes. It will thicken as it cools and is ready to serve with a scoop of vanilla ice cream or a dollop of whipped cream.