In the bowl of a food processor, pulse together the flour, sugar, baking powder, baking soda, and salt. Pulse the butter into the dry ingredients until course crumbs form. Stir in the milk mixture gently until a soft dough forms.
Stir the lemon juice and milk together and allow to sit for 5 minutes.
In a large baking dish, toss the blueberries, ½ cup sugar and tapioca together.