three 6-cavity nonstick doughnut pans, each with 2 1/4-inch diameter wells
For the doughnuts: Preheat the oven to 350 degrees F. Grease three 6-cavity nonstick doughnut pans (each with 2 1/4-inch diameter wells) with nonstick cooking spray.
Whisk together the granulated sugar, egg, milk, sour cream, vanilla, lemon zest, lemon juice and oil in a medium bowl. Set aside.
In another medium bowl, whisk together the flour, baking powder, baking soda and salt. Slowly add to the wet ingredients and whisk just to combine. Gently fold the frozen berries into the batter.
Spoon the batter into the prepared doughnut pans and bake until a toothpick inserted in the center comes out clean, 12 to 14 minutes. Let the doughnuts cool in the pans for 10 minutes, then remove the doughnuts to a wire rack to cool completely before glazing.
For the glaze: Whisk together the confectioners' sugar and raspberry juice in a medium bowl until smooth. Dip just the top of each cooled doughnut into the glaze and let the excess drip off.
For the topping: Decorate the glazed doughnuts with the sprinkles or crushed freeze-dried berries.