Preheat the oven to 350 degrees F (175 degrees C). Grease a 9-inch square baking pan.

Beat sugar and butter together in a mixing bowl using an electric mixer until light and fluffy. Beat in eggs and vanilla extract until well combined.

Sift flour and baking powder together in a separate bowl; add to creamed mixture until incorporated.

Pour in milk, lemon zest, and lemon juice; mix until smooth.

Spoon batter into the prepared pan.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 35 minutes.

Let cake cool before cutting into squares. Enjoy!