Preheat the oven to 350°F (175°C). Grease and flour two 8-inch (20 cm) round cake pans and line the bottoms with parchment paper.
In a medium bowl, whisk together the sifted all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat the softened unsalted butter and granulated sugar together using an electric mixer on medium speed until light and fluffy, about 3 to 4 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the finely grated lemon zest, fresh lemon juice, and pure vanilla extract until combined.
Reduce the mixer speed to low and alternately add the dry ingredients and buttermilk in three additions, beginning and ending with the dry ingredients. Mix just until combined after each addition; do not overmix.
Divide the batter evenly between the prepared cake pans and smooth the tops with a spatula.
Bake in the preheated oven for 28 to 32 minutes, or until a toothpick inserted into the center of the cakes comes out clean.
Remove the cakes from the oven and allow them to cool in the pans for 10 minutes.
Run a knife around the edges of the pans to loosen the cakes, then invert them onto wire racks to cool completely before frosting or layering.