Preheat the oven to 375 degrees F (190 degrees C).
Toss sliced apples with lemon juice to prevent browning.
Mix flour, rolled oats, wheat and barley nugget cereal, melted butter, 1/4 cup white sugar, and 1/4 cup brown sugar together in a large bowl.
Melt 2 tablespoons butter in a large skillet over medium heat. Stir 1/3 cup brown sugar, 1/3 cup white sugar, and cinnamon into melted butter until sugar begins to dissolve, 3 to 4 minutes. Add apples and water; continue cooking and stirring until apples soften and are coated with sauce, 4 to 5 minutes.
Pour apples and sugar mixture into a 2 quart baking dish. Sprinkle topping evenly over the apple filling.
Bake in the preheated oven until the top is browned and the filling is bubbling up around the edges, 25 to 30 minutes. Cool for 10 to 15 minutes.
