Preheat oven to 350°F and line a loaf pan with parchment paper.
In a large bowl, whisk together flour, baking powder, salt, and poppy seeds; set aside.
Smash blackberries in a separate bowl using a fork and set aside.
In another large bowl, whisk avocado oil, maple syrup, vanilla extract, lemon juice, lemon zest, eggs, and 1/3 cup almond milk until combined.
Gradually add dry ingredients into the wet mixture, stirring gently until just combined.
Divide batter into two bowls; mix reserved tablespoon of smashed blackberries into one bowl to create a purple batter.
Add remaining 3 tablespoons almond milk to second bowl; mix well.
Alternate spooning layers of each batter into the prepared loaf pan.
Bake for 25 minutes, rotate the pan, then bake for another 25 minutes or until a toothpick inserted into the center comes out with a few crumbs.
Let the loaf cool; meanwhile, mix reserved smashed blackberries with powdered sugar, lemon zest, and lemon juice to make icing.
Drizzle the icing over the cooled loaf before serving.