Preheat the oven to 350°F and line a 1 lb loaf pan with parchment paper or grease well. Set aside.
In a large bowl, combine the granulated sugar and lemon zest. Use your fingers to rub the sugar and the lemon zest together. This will help the zest to release and infuse the sugar with lemon flavor.
Add the melted butter to the sugar and mix well. Add the vanilla extract and the eggs in, one at a time, mixing well between each addition.
Add the sour cream, milk and lemon juice. Mix to combine.
Add the all purpose flour, baking powder, and salt. Mix until the batter is smooth and no lumps remain. Do not over mix.
Pour the batter into the prepared loaf pan and bake at 350°F for 45 minutes to 1 hour, or until a knife inserted into the middle comes out mostly clean.
Make the lemon glaze while the bread cools. Combine all the ingredients for the lemon icing in a bowl and whisk together. If the glaze seems too thick, add in an additional teaspoon of milk until it reaches a drip-able consistency.
Once the bread is cool, remove from the pan and pour the glaze over the bread, allowing it to drip down the sides. Let the glaze sit for a few minutes to set before slicing and enjoying!