Preheat the oven to 350°F and coat an 8x8-inch baking pan with nonstick spray. Ensure the spray is gluten-free if necessary.
In a large mixing bowl, combine the frozen mixed berries, cornstarch, sugar, and lime juice. Toss until the berries are evenly coated. Transfer the mixture to the prepared baking pan, ensuring all sugar and cornstarch from the bowl are included.
Using the same bowl, prepare the topping by mixing the quick oats, old-fashioned oats, both sugars, and kosher salt. Add the butter pieces to the mixture, and using a pastry blender or your hands, work the butter into the oat mixture until fully incorporated.
Spread the topping evenly over the berries in the baking pan. Bake on the middle rack for 55–60 minutes, or until the berries are bubbling and the topping is golden brown. If the topping starts to over-brown during baking, cover the pan with aluminum foil and continue cooking.