Preheat the oven to 400°F (200°C) and line a medium-sized baking sheet with parchment paper.
Combine the flour, cane sugar, baking powder, and lemon zest in a large bowl. Cut the cold butter cubes into the dry ingredients until it’s crumbly. Use a fork or pastry cutter for this.
Stir in the vegan yogurt just until everything is moistened. With floured hands, fold the dough together some more to make sure the ingredients are combined. Then, gently fold in the blackberries.
Move the scone dough to a floured surface such as a cutting board. Without overworking it, form the dough into a circular disc that's about 1 inch in height. Place the scone disc in the freezer for 10 minutes.
Remove the dough from the freezer. Slice it into 8 wedges and place them an inch apart on the baking sheet. Brush the tops with plant-based milk. Bake the scones on the top rack for 20-25 minutes. Start checking on them after 15 minutes to prevent them from burning.
Remove the scones from the oven when they are golden brown and place them on a cooling rack. Make the icing by whisking together the lemon juice and powdered sugar. Drizzle it over the scones once they have cooled down.