Adjust oven rack to middle position and heat oven to 350℉/180℃. Grease a loaf pan, 8½ x 4¼-inch or 9 x 5-inch, or line it with parchment paper.

In a medium bowl, sift together dry ingredients: flour, baking powder, baking soda, and salt. In a small bowl, mix together buttermilk and lemon juice. Set bowls aside. In another small bowl, toss together sugar and lemon zest until well combined, set aside.

In a stand mixer fitted with the paddle attachment, beat together butter and sugar mixture on medium speed for 3 minutes until light and fluffy. Occasionally scrape down the sides and bottom of the bowl. Add eggs, one at a time, beating well after each addition. Beat in vanilla extract. On low speed, beat in the flour mixture in 3 additions, alternating with the buttermilk mixture in 2 additions, starting and ending with the flour. Do not over-mix.

Scrape batter into prepared pan and smooth the top. Bake for 40-60 minutes or until a skewer inserted into the center of the cake comes out clean. If the top is browning too fast while baking, cover pan loosely with aluminum foil.

While cake is in the oven, prepare the syrup. In a small saucepan, combine sugar, lemon juice, and water. Cook on medium-low heat until sugar dissolves and syrup forms. Set aside to cool.

When the cake is done, allow to cool for 10 minutes, then remove from pan and set on a wire rack. Place a tray or pan underneath the wire rack. Poke cake with a toothpick, then brush top and sides with syrup. Allow cake to cool to room temperature.

In a small bowl, combine sugar, lemon juice, and milk, and whisk until smooth. Add more lemon juice or sugar as necessary until you get a thick yet pourable consistency. Pour over top of cake and let drizzle down the sides. Allow glaze to set, 15-30 minutes. Slice and serve.