Combine non-dairy milk with lemon juice and set aside until it curdles to create vegan buttermilk.
Preheat oven to 350°F (175°C). Grease and line two 8-inch (20cm) pans with parchment paper, cut to fit the pan. (I don't recommend skipping this step or the cakes could stick to the pan.)
In a large bowl whisk together flour, baking powder, baking soda, sugar, and salt.
Stir the oil, vanilla and lemon zest into the vegan buttermilk. Then pour it into the flour mixture and mix everything just until the ingredients are combined. (Don't overmix or your cakes will be dense).
Divide the batter evenly between the two cake pans and bake for about 30 minutes or until a toothpick inserted into the center comes out clean. (Don't overbake or your cakes will get dry.)
Let cool completely. (Optionally, wrap each cake in plastic wrap and refrigerate at least 2 hours until well chilled because this makes them easier to cut evenly.)