Preheat oven to 350°F (175°C). Spray a 8-inch baking pan with cooking spray. Line the bottom with circle of parchment paper.
Stir black sesame almond milk and vinegar together in a large glass measuring cup. Set aside.
In a large mixing bowl, whisk flour, sugar, baking soda, baking powder, and salt together. Set aside.
Briskly mix vegetable oil, water, lemon juice and vanilla extract into black sesame almond milk mixture using a fork. Using a rubber spatula, stir milk mixture into flour mixture until batter is lump-free. Pour batter into the prepared baking pan.
Bake in the preheated oven until a toothpick inserted in the center of the cake comes out clean, about 30-35 minutes. Start checking to see if cake is done at 30 minutes.
Allow cake to cool in pan over a cooling rack for 15 minutes, then turn cake out of pan to cool completely before frosting.