Heat the oven to 375°F and butter a 9-by-13-inch baking dish.
Toss the peaches with granulated sugar, cornstarch, lemon juice and 1/4 teaspoon salt, then spread in the dish.
Stir the oats, flour, brown sugar, cinnamon and 1/2 teaspoon salt together.
Pour in the melted butter and squeeze the mixture until some large clumps form.
Scatter the topping evenly over the peaches without packing it flat.
Bake for 40 to 44 minutes until the crumbs are browned and peach filling bubbles at the center; cool 25 minutes.