Preheat your oven to 350°F (175°C). Toss sliced peaches with sugar, lemon juice, and cinnamon in a large bowl until well coated.
Transfer the peach mixture into a buttered baking dish, spreading it into an even layer.
In a separate bowl, combine flour, brown sugar, and oats if using. Add the cold diced butter and cut it into the dry ingredients with a pastry cutter or fork until the mixture resembles coarse crumbs.
Evenly sprinkle the crumble topping over the peaches, covering the surface completely.
Bake uncovered in the preheated oven for about 40 minutes, until the topping is golden brown and the filling is bubbling around the edges.
Remove from oven and let it cool slightly before serving. The topping will be crisp and crunchy with juicy, tender peaches underneath.