Preheat the oven to 350 degrees F (175 degrees C). Line a muffin tin with parchment paper liners.
Stir sugar, flour, and oats together in a small bowl until combined. Work butter into the dry ingredients until it resembles damp sand. Set the topping aside while you prepare the muffin batter.
Stir together applesauce, sugar, egg, and lemon zest in a large bowl. Add lemon juice and sour cream and stir until combined. Add flour, baking powder, and salt. Stir everything together until just combined.
Spoon batter into the prepared muffin cups, filling each halfway. Sprinkle the topping on each muffin until completely covered.
Bake in the preheated oven until a toothpick comes out clean, 20 to 25 minutes. Cool in the tin for about 10 minutes before serving.
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