Preheat oven to 350°F and lightly grease a donut pan. In a mixing bowl, rub together the sugar and lemon zest to release the flavor. Add flour and baking powder and mix to combine.
In a separate mixing bowl, whisk together non-dairy milk, vanilla, lemon juice, applesauce, and melted butter. Pour wet ingredients into dry ingredients and mix until just combined.
Pipe or spoon batter into donut pan, filling each about 3/4 full.
Bake for 10–13 minutes, or until set and lightly golden.
Let donuts cool completely before removing from pan.
Whisk together glaze ingredients until smooth.
Dip donuts into glaze and let set before serving.