Preheat your oven to 350°F. Grease a 9x13-inch baking pan or two 9-inch round cake pans.

In a bowl, whisk flour, baking powder, and salt. Set aside.

In a large bowl, cream softened butter and sugar with an electric mixer until light and fluffy, about 2 minutes.

Add the eggs to the butter mixture one at a time, beating well after each addition.

Mix in the lemon juice, lemon zest, and vanilla extract until well combined.

Slowly incorporate the dry ingredient mixture and milk into the batter, starting and finishing with the dry ingredients. Stir until barely blended; avoid overmixing.

Pour the batter into the prepared pan(s), smoothing the top with a spatula.

Place in the preheated oven and bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cake to cool in the pan for 15 minutes, then transfer to a wire rack to cool completely.

In a small bowl, whisk together the powdered sugar and lemon juice until smooth. Slowly add the milk. If the glaze is too thick, add more lemon juice or milk until you reach your desired taste and consistency.

Drizzle the glaze over the cooled cake. Allow it to set before serving.