*Have all ingredients at room temperature.* Preheat oven to 350℉/177℃. Grease a 9 x 5 inch loaf pan and line with parchment paper.
In a large bowl combine sugar and lemon zest. Mix this together well, massaging the lemon zest into the sugar. This will release the flavorful oils in the lemon zest.
Next add all purpose flour, baking powder, baking soda and salt. Mix together well.
Add butter and oil. Mix on low speed with electric mixer until the ingredients are evenly distributed and it resembles wet sand. If necessary, break down any bits of butter with your fingers that are not incorporating.
Add lemon juice and eggs. Mix until a smooth, thick batter forms, about 1 minute. Add sour cream and vanilla. Beat on low speed until the batter is just combined and smooth, about 30-45 seconds.
Spread batter into prepared loaf pan. Bake for 45-50 minutes or until the loaf is golden and the middle springs back when lightly pressed. A toothpick inserted in the center should also come out clean. Cool 10 minutes in pan before lifting out onto a wire rack to cool completely. Drizzle with glaze, allowing some to drip down the sides. You can also glaze the loaf while it's still a little warm if you want a more melted look. Allow glaze to set before slicing.
GLAZE
In a medium bowl combine confectioner's sugar and salt. Gradually add lemon juice to form a very thick glaze. The glaze should be of almost spreading consistency, thick enough that it sets up yet still runny enough to drizzle.