To make the vegan lemon cake: Preheat the oven to 350º F. Line three 9" cake pans with parchment paper rounds and spray generously with cooking oil. Set aside.
In a medium bowl, stir together the flour, baking powder, baking soda, and salt. In a separate bowl combine the non-dairy milk and lemon juice. Set aside.
In a stand-up mixer or an electric handheld mixer, beat together the butter, sugar, lemon zest, and extracts until light and fluffy. With the motor running, add the applesauce scraping down the sides as necessary. The mixture will appear to have separated at this point, but it will come back together. Alternating wets (soymilk and lemon juice) and dries (flour mixture) add in three batches, scraping down the sides as needed, ending with the flour mixture until it just comes together. Do not over-mix.
Pour batter into prepared cake pans and smooth top. Bake until cake is golden brown (about 20-25 minutes), and a toothpick comes out clean when inserted in the middle. Remove from the oven and let cool for 60 minutes. Flip out onto wire racks and allow the loaf to cool completely. To make the Cream Cheese Frosting, in a stand-up mixer with the paddle attachment, beat together vegan cream cheese and vegan butter until well combined, scraping down the sides as necessary. Add lemon extract and combine it. With the mixer on its lowest setting, slowly add the powdered sugar one cup at a time, stopping to scrape down the sides between cups. Once all the powdered sugar is added, turn up the speed to medium and mix until smooth and creamy. To assemble the cake, place about 1 ½ cups of cream cheese frosting on the bottom layer of lemon cake, smooth oven evenly with an offset spatula and top with a second layer of cake. Repeat with a third layer if necessary. Coat the entire cake in cream cheese frosting and top with lemon wedges.