Preheat oven to 350°F. Lightly grease two 6-cavity donut pans.
Whisk flour, sugar, baking powder, baking soda, salt, and nutmeg in a large bowl.
Stir lemon juice into the milk. Let sit 2 minutes to lightly thicken.
Whisk the milk mixture with beaten eggs, vanilla, and melted butter until smooth.
Fold wet ingredients into dry just until combined. Stir in lemon zest; do not overmix.
Pipe or spoon batter into pans, filling each well about three-quarters full.
Bake 10–12 minutes, until the tops spring back and edges are lightly golden.
Cool donuts in the pans 5 minutes, then transfer to a rack to finish cooling.
Whisk powdered sugar, lemon juice, milk, melted butter, vanilla, and zest until silky and pourable.
Dip warm donuts into the glaze, letting excess drip. Set on a rack to firm up.