Preheat oven to 350* F. Prepare loaf pan by greasing it with coconut oil or non stick spray. Insert a parchment sling for easy removal. See above photos for reference.
In a large bowl, combine sugar, oil, non dairy yogurt, non dairy milk, lemon juice, vanilla and lemon zest. Whisk well to combine.
Fit a mesh sifter over the top of the mixing bowl containing the wet ingredients, being sure to not allow the bottom of the sifter to touch the wet ingredients.
Add the flour, baking powder, baking soda and salt to the sifter and sift the dry ingredients into the wet ingredients. Whisk until just combined.
Add the blackberries and fold to distribute.
Pour batter into a loaf pan and bake in a 350*F oven for 60-65 minutes or until a toothpick inserted into the center of the loaf comes out clean with a few moist crumbs attached.
Cool completely, remove from the pan using the parchment sling and place onto a cutting board to slice and serve.
Store in an airtight container at room temperature for up to 4 days.