Adjust oven rack to middle position and heat oven to 350°F/180°C. Grease well a 12-cup (10-inch) Bundt pan and set aside.
To make the cake: In a medium bowl, sift together flour, baking powder, baking soda, and salt. In a small bowl, mix together buttermilk/sour cream, lemon juice, and vanilla extract. Set bowls aside.
In a standing mixer fitted with the paddle attachment, beat together butter, sugar, and lemon zest on medium speed for 3-4 minutes until fluffy. Occasionally scrape down the sides and bottom of the bowl. Add eggs, one at a time, beating well after each addition. On low speed, beat in the flour mixture in 3 additions, alternating with the lemon juice 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 45-55 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. Allow cake to cool for 10-15 minutes, then remove from pan, carefully inverting it onto a plate.
Meanwhile, make the syrup: In a small saucepan, combine sugar and lemon juice. Cook on medium-low heat until sugar dissolves and syrup forms. After inverting the cake to a plate, brush top and sides of the cake evenly with syrup. Use all syrup. Allow cake to cool to room temperature.
To make the glaze: In a small bowl, combine sugar, lemon juice, and milk, and whisk until smooth. Add more milk 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.
The cake is best served at room temperature. Store cake in an airtight container in the fridge for up to 5 days. Leftovers can be frozen for up to 2 months.