Preheat the oven to 350 degrees F. Grease two 8 inch cake pans, line with parchment rounds (I cut them out myself to fit the bottom of the pans, prevents sticking), and grease the parchment paper as well. Sprinkle lightly with flour.
In a measuring cup, combine the almond milk and apple cider vinegar. Let sit a few minutes until it curdles (this is your vegan buttermilk).
In a medium sized bowl, drain the chickpeas to collect the liquid from the can. (Rinse the chickpeas and refrigerate for another use) With a hand mixer, mix on low-medium speed for about 1 minute, until light and foamy. Set aside.
In a large bowl, add the softened butter, sugar and lemon zest. Stir to combine. Beat on medium speed with the handheld mixer until light and fluffy, about 3 minutes. Now add in the lemon and vanilla extracts and beat to combine.
On low speed, add in the almond milk mixture and aquafaba and mix. Now add the flour, sprinkle the baking powder and salt on top of the flour and mix on low until well combined, about 1-2 minutes, scraping the sides as needed with a spatula.
Divide the batter equally in the prepared pans. Bake for 30-35 minutes, until a toothpick inserted comes out clean. Let cool on wire racks for 5-10 minutes, then run a knife around the edges to loosen, and carefully invert the cakes onto your hand. Remove the parchment paper and place on a wire rack to cool completely.
Make the frosting: Using a standing mixer or handheld mixer, beat the vegan butter until light and fluffy, about 2 minutes. Reduce the speed, add in the 2 cups of the powdered sugar, lemon juice, lemon zest and vanilla extract. Beat on low, then switch to medium speed and beat until light and fluffy, about 2 minutes. Now add in the remaining 2 cups powdered sugar and mix. If the frosting seems too thick, add a tablespoon at a time of non-dairy milk. If the frosting seems too thin, add more powdered sugar until a desirable consistency is reached.
Frost the cake: Place one of the cake layers on your cake stand or plate. Frost the top evenly. Place the second cake layer on top. Top the second layer with more frosting, and frost the sides as well. Decorate as desired and serve!