Preheat the oven to 350°F (175°C). Grease and flour the two 9-inch round cake pans.

In a mixing bowl, combine the all-purpose flour, granulated sugar, baking powder, and salt. Mix well.

Add the softened butter to the dry ingredients and beat with an electric mixer on medium speed until the mixture resembles coarse crumbs.

In a separate bowl, whisk together the eggs, milk, lemon juice, lemon zest, and vanilla extract. Slowly add this mixture to the dry ingredients and mix until just combined. Do not overmix; a few lumps are okay.

Divide the batter evenly between the two prepared cake pans.

Bake in the preheated oven for 30-35 minutes or until a toothpick inserted into the center comes out clean.

Once baked, remove the cakes from the oven and let them cool in the pans for 10 minutes. Then, transfer them to a cooling rack to cool completely.

While the cakes are cooling, prepare the lemon glaze by combining powdered sugar and lemon juice in a bowl. Mix until smooth and the desired consistency is reached.

Once the cakes are completely cool, place one layer on a serving plate, drizzle half of the lemon glaze on top, then place the second layer on top and drizzle the remaining glaze over it.

Slice and serve the cake, or refrigerate until ready to serve.