Preheat oven to 375 degrees F (190 degrees C). Grease a 9x13-inch baking dish with butter.
Beat 2 cups whole wheat flour, rolled oats, butter, 1/2 cup brown sugar, 1/2 cup white sugar, 1 teaspoon cinnamon, and 1/4 teaspoon kosher salt in a bowl with an electric mixer on medium speed until the mixture is pea-size and crumbly, 3 to 5 minutes. Refrigerate until ready to use.
Combine apples, blueberries, 1/4 cup brown sugar, 1/4 cup white sugar, 2 tablespoons whole wheat flour, lemon juice and zest, 1 teaspoon cinnamon, and nutmeg in a large bowl; transfer to prepared baking dish. Sprinkle crumble mixture over fruit mixture.
Bake in preheated oven until topping is browned and fruit is bubbly, 35 to 45 minutes.