Preheat your oven to 350°F (175°C). In a large mixing bowl, toss sliced peaches with sugar, cinnamon, and lemon juice until evenly coated. Spread the peach mixture evenly into a buttered baking dish.
In another bowl, combine oats, flour, brown sugar, salt, and cinnamon. Mix to combine.
Add cold butter cubes to the dry ingredients. Using your fingertips or a pastry cutter, cut the butter into the mixture until it resembles coarse crumbs with some pea-sized pieces.
Sprinkle the crumbly topping evenly over the peaches in the baking dish, covering all the fruit surface.
Bake in the preheated oven for about 35 minutes, or until the topping is golden brown and the filling is bubbling around the edges.
Remove the dish from the oven and let it cool slightly before serving. The topping will be crisp and crunchy while the peaches will be tender and juicy, creating a warm, textured dessert.