Preheat the oven to 350°F (175°C). Lightly grease an 8x8-inch baking dish with butter or nonstick cooking spray.
Toss the diced apples with the lemon juice and set aside.
In a large mixing bowl, whisk together the rolled oats, baking powder, cinnamon, nutmeg, cloves (if using), and salt.
In a separate bowl, whisk together the eggs, milk, maple syrup, brown sugar, vanilla extract, and melted butter until smooth.
Pour the wet ingredients into the dry ingredients and stir just until combined.
Fold half of the diced apples into the oatmeal mixture.
Pour the mixture into the prepared baking dish and spread it into an even layer.
Scatter the remaining apples evenly over the top.
If making the topping, stir together the rolled oats, brown sugar, cinnamon, and melted butter until evenly coated. Sprinkle over the oatmeal.
Bake for 40–45 minutes, or until the edges are lightly golden and the center is just set. A toothpick inserted into the center should come out mostly clean with a few moist oat flakes attached.
Let the baked oatmeal rest for 15 minutes before serving.
Serve warm with maple syrup, vanilla yogurt, chopped toasted pecans, or a splash of milk if desired.