Preheat oven to 375 degrees. Grease and flour a 9x5-inch loaf pan; set aside.
In a medium bowl, sift together flour, baking powder, salt and baking soda; set aside.
In large bowl, beat together the sugar and oil until light and fluffy. Add eggs, lemon juice and vanilla, beat until well combined.
Slowly add to dry ingredients to the wet, beating until just combined.
Gently fold in frozen blackberries, chopped nuts and lemon zest.
Pour batter into prepared loaf pan. Bake for 20 minutes at 375 degrees then reduce heat to 350 degrees; continue to bake until golden brown and toothpick inserted in center of loaf comes out clean, about 40-45 minutes longer. Cool in the pan for 10 minutes, then transfer to wire rack and cool completely before serving.
Cook's Note: Freeze your blackberries on a cookie sheet, they won't bleed as much juice when stirring into the batter.