Gather the ingredients. Preheat the oven to 350 degrees F (175 degrees C).
To make the scones: Whisk flour, sugar, baking powder, baking soda, and salt together in a large bowl. Cut in cold butter with 2 knives or a pastry blender until mixture resembles coarse crumbs. Whisk milk, lemon juice, lemon zest, and vinegar in a small bowl; stir into flour mixture until dough is moistened.
Turn dough out onto a lightly floured surface and knead briefly, 5 or 6 turns.
Pat or roll dough out into a 1-inch-thick round. Cut into 10 wedge-shaped pieces; arrange 1 inch apart on a baking sheet.
Bake in the preheated oven until bottom edges are golden brown, 12 to 15 minutes. Cool scones on a wire rack for 15 minutes.
Meanwhile, to make the lemon glaze: Stir confectioners' sugar, melted butter, lemon juice, and vanilla together in a bowl until smooth. Stir water into sugar mixture, 1 tablespoon at a time, to make a glaze; drizzle glaze over warm scones.