Preheat oven to 375°. In a large bowl, whisk the first five ingredients. In another bowl, whisk eggs, milk, melted butter and lemon juice until blended. Add to flour mixture; stir just until moistened. Fold in blackberries.
Fill greased or foil-lined muffin cups three-fourths full. Bake 15-18 minutes or until a toothpick inserted in center comes out clean. Cool 5 minutes before removing from pan to a wire rack.
In a small bowl, mix confectioners' sugar, melted butter and enough lemon juice to reach desired consistency. Drizzle over warm muffins. If desired, sprinkle with lemon zest.