Preheat your oven to 350°F (175°C). Grease and flour a standard 9x5 inch loaf pan, or line it with parchment paper.

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

In a large bowl, cream together the softened butter and granulated sugar using an electric mixer until light and fluffy (about 3 minutes). Beat in the eggs one at a time, ensuring each is fully incorporated before adding the next. Mix in the lemon zest and fresh lemon juice.

Alternate adding the dry ingredients and the buttermilk to the wet ingredients, beginning and ending with the dry ingredients (1/3 dry, 1/2 buttermilk, 1/3 dry, 1/2 buttermilk, 1/3 dry). Mix only until just combined; do not overmix.

Gently fold in the floured blackberries until evenly distributed throughout the batter. Pour the batter into the prepared loaf pan and spread evenly. Bake for 50-60 minutes, or until a wooden skewer inserted into the center comes out clean. If the top browns too quickly, loosely tent with foil.

Let the cake cool in the pan for 15 minutes before carefully turning it out onto a wire rack to cool completely.

While the cake cools, prepare the glaze: Whisk together the powdered sugar and 2 tablespoons of lemon juice until smooth. Add more juice, 1 teaspoon at a time, until the glaze is thick but pourable. Drizzle generously over the cooled loaf cake.