Preheat the oven to 350°F (175°C) and grease a 9x5-inch loaf pan with butter or non-stick spray.

In a medium mixing bowl, whisk together the flour, baking powder, and salt.

In a large mixing bowl, combine the melted butter and granulated sugar, then whisk in the eggs, 2 tablespoons of lemon juice, and the lemon zest.

Gradually add the dry ingredients to the wet ingredients, alternating with the milk, and stir until just combined.

Gently fold the blackberries into the batter using a spatula to avoid crushing the fruit.

Pour the batter into the prepared loaf pan and smooth the top.

Bake for 55 to 65 minutes, or until a skewer inserted into the center comes out clean.

Cool the bread in the pan for 10 minutes, then transfer to a wire rack to cool completely.

In a small bowl, whisk the confectioners' sugar and the remaining 1 tablespoon of lemon juice until smooth, then drizzle over the cooled bread.