Preheat the oven to 350°F (177°C). Grease three 8-inch cake pans and line with parchment paper.
Whisk together the dry ingredients (flour, baking soda, baking powder, and salt). Set aside.
In a large bowl, mix sugar and butter until creamy (about 3 mins).
Add eggs and 2 teaspoons vanilla extract to the mixture above, and beat until fully mixed (2-3 mins).
Gradually add the dry ingredients and mix at low speed until blended. Then, add the lemon zest, juice, and milk and mix until combined.
Divide batter evenly among prepared pans. Bake for 20-25 minutes until golden and cooked through. Cool in pans on a wire rack.