Preheat your oven to 375°F (190°C) and grease a baking dish with butter or non-stick spray.
In a large mixing bowl, gently toss the sliced peaches with lemon juice and half of the brown sugar until well coated. Spread the fruit evenly into the prepared baking dish.
In a separate bowl, combine rolled oats, flour, remaining brown sugar, and cinnamon, stirring to blend.
Add the cold, cubed butter to the dry mixture. Use a pastry cutter or your fingers to cut the butter into the mixture until it resembles coarse crumbs.
Sprinkle the oat topping evenly over the peaches, ensuring full coverage to create a crunchy crust.
Bake in the preheated oven for about 35 minutes, or until the topping is golden brown and the peaches are bubbling around the edges.
Remove from oven, let cool slightly, and serve warm with ice cream or whipped cream if desired.
