Preheat the oven to 350˚F / 175˚C. Grease a 9x13" baking dish and line it with parchment paper.
In a large bowl, cream together softened butter and sugar. Add vanilla extract, lemon extract, and lemon zest. Mix in applesauce.
In a separate bowl, stir together flour, baking powder, baking soda, and salt.
Gradually add the dry mixture to the wet mixture, alternating with milk and lemon juice, until well combined.
Spread the batter evenly in the prepared baking pan. Bake for 34-38 minutes or until a toothpick inserted into the center comes out clean. Allow the cake to cool completely before frosting.