Preheat oven to 350°F (175°C). Grease and flour a 9-inch round cake pan (or line with parchment).
In a large bowl, cream butter and sugar until light and fluffy.
Add eggs one at a time, mixing well after each addition. Stir in the lemon zest.
In a separate bowl, whisk together flour, baking powder, and salt.
Gradually add dry ingredients to the butter mixture, alternating with milk and lemon juice. Mix until just combined.
Pour the batter into the prepared pan and bake for 30–35 minutes, or until a toothpick inserted in the center comes out clean.
Allow cake to cool completely on a wire rack.
For the glaze, whisk together powdered sugar and lemon juice until smooth. Drizzle over the cooled cake.