Heat the oven to 350°F. Line two 9-inch round cake pans with parchment paper and lightly coat the sides with neutral oil.
Whisk the cake flour, baking powder, baking soda, and salt in a medium bowl. In a measuring cup, stir together the soy milk, lemon juice, and vanilla extract.
Beat the dairy free butter, granulated sugar, and lemon zest for 3 to 4 minutes, until pale and fluffy. Beat in the eggs one at a time, scraping the bowl after each addition.
Add the flour mixture in three additions, alternating with the lemon and soy milk mixture in two additions. Mix on low speed only until the batter is smooth.
Divide the batter between the prepared pans and bake for 27 to 32 minutes, until a toothpick inserted in the center comes out clean. Cool for 15 minutes in the pans, then transfer the layers to wire racks to cool completely.
Beat the dairy free butter for 2 minutes. Gradually add the powdered sugar, then beat in the lemon juice, soy milk, lemon zest, vanilla extract, and salt until fluffy and spreadable.
Place one cake layer on a serving plate and cover it with lemon frosting. Add the second layer, frost the top and sides, and refrigerate for 20 minutes to set the finish before serving.