Preheat the oven to 350℉. Grease a 9x5-inch loaf pan and line it with parchment paper, leaving an overhang on the sides for easy removal.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. In a large mixing bowl, combine the sugar and lemon zest, rubbing the zest into the sugar with your fingers until fragrant.
Add the eggs one at a time, beating well after each addition until light and fluffy. Stir in the sour cream, lemon juice, milk, vegetable oil, and vanilla extract until fully combined.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Pour the batter into the prepared loaf pan and smooth the top.
Bake for 55-60 minutes, or until a toothpick inserted in the center comes out clean. Cool in the pan for 20 minutes, then lift out and transfer to a wire rack to cool completely.
To make the glaze, whisk together powdered sugar and lemon juice in a medium bowl until smooth, adjusting the consistency with more lemon juice if needed.
Once the cake is completely cool, drizzle the glaze over the top and let it drip down the sides. Allow the glaze to set for 30 minutes before slicing.