Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, mixing well after each addition. Then, mix in the lemon zest, lemon juice, and vanilla extract.
In a separate bowl, whisk together the flour, baking powder, baking soda, salt, and cream of tartar.
Gradually add the dry ingredients to the wet mixture, alternating with the buttermilk. Begin and end with the dry ingredients, mixing until just combined.
Divide the batter evenly between the prepared cake pans. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cakes to cool in the pans for 10 minutes before transferring them to wire racks to cool completely.
While the cakes are cooling, prepare the frosting. In a large bowl, beat together the softened cream cheese and butter until smooth.
Gradually add the powdered sugar, mixing until well combined. Then, mix in the lemon juice, lemon zest, and vanilla extract until smooth and creamy.
Once the cakes are completely cool, place one layer on a serving plate. Spread a generous amount of frosting on top, then place the second layer on top and frost the top and sides of the cake.
Serve immediately or refrigerate for up to 2 hours to set the frosting before serving.