Preheat your oven to 350°F (175°C) and grease a 9-inch round cake pan.
In a mixing bowl, cream the softened butter and sugar until light and fluffy.
Add the eggs one at a time, mixing well after each addition.
Stir in the vanilla extract and lemon zest.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, alternating with the milk.
Mix until just combined, then fold in the fresh lemon juice.
Pour the batter into the prepared cake pan and smooth the top.
Bake for 30-35 minutes, or until a toothpick inserted comes out clean.
Let the cake cool in the pan for 10 minutes before transferring to a wire rack to cool completely.