Preheat your oven to 350°F (175°C). Grease and flour a 9x13-inch baking pan or line it with parchment paper.
In a large mixing bowl, cream together the softened butter and sugar until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, mixing well after each addition. Then, stir in the lemon zest and vanilla extract.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the butter mixture, alternating with the milk. Start and end with the flour mixture. Mix until just combined.
Stir in the fresh lemon juice until fully incorporated.
Pour the batter into the prepared baking pan and smooth the top with a spatula.
Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then transfer it to a wire rack to cool completely.