Preheat oven to 350 degrees. Line muffin tin with baking cups.
In a medium bowl, whisk together flour, oats, baking powder, and cinnamon.
In a separate bowl, whisk together sugar, eggs, butter, and milk.
Stir wet ingredients into dry ingredients, then stir in apple.
Divide batter evenly between muffin cups.
Whisk together oats, flour, sugar, and salt. Stir in butter until clumpy.
Sprinkle each muffin with crumb topping. Bake about 20 minutes. Let cool on a wire rack.
To make the icing, cream melted butter and cream cheese for 2 minutes until very fluffy. Add powdered sugar and lemon juice and mix well.
Drizzle icing over top of each muffin.