Preheat oven to 350F and spray donut baking pan with nonstick spray.
In a large bowl, mix together the flour, baking powder, salt, and baking soda.
In a medium bowl, whisk together the sugar, milk, yogurt, egg, butter, vanilla, lemon juice, and lemon zest.
Slowly whisk the sugar mixture into the flour mixture until fully combined.
Gently fold in the blackberries to the batter until evenly distributed.
Put the batter in a piping bag or zip top bag.
Pipe batter into each well (will make about 6 regular sized donuts).
Bake for 8-10 minutes, until lightly golden.
Remove from oven and transfer to cooling rack. Let completely cool before adding glaze.