Mix non-dairy milk and lemon juice in a small cup and set aside to create vegan buttermilk.
Preheat oven to 400°
Whisk together flour, baking powder, baking soda, sugar, and salt.
Cut the chilled butter into the dry ingredients using a pastry blender, fork, or your fingers. Work the butter into the dry ingredients until the mixture becomes grainy in appearance.
Once the butter has been fully cut into the dry ingredients, add the sourdough starter to the mixture and mix gently, until the dry ingredients are just incorporated. The mixture will come together, but still, be slightly dry.
Add in the non-dairy milk one tablespoon at a time, mixing VERY gently until the biscuit dough just comes together. Overmixing will lead to tough, dense biscuits!
Generously flour your work surface and roll out the dough until it is 1-inch thick (NO THINNER). Using a 3" biscuit cutter, cut the biscuits, pressing straight down into the dough with the cutter without twisting. Continue until you have cut 6-7 biscuits. FOr an extra biscuit, you can arrange the scraps into a biscuit.
Place all the biscuits onto a parchment-lined baking sheet so that the biscuits are slightly toughing. If desired, brush the biscuit tops with extra soymilk or melted vegan butter.
Bake at 400° for 15 minutes until the biscuit tops are golden brown.