Preheat oven to 325 F. Grease a 9x5-inch loaf pan; set aside.
In a medium bowl, whisk together flour, baking soda, baking powder, and salt. Set aside.
In a large bowl, whisk vegetable oil, sour cream, and sugar together until combined.
Whisk in eggs.
Add lemon juice and vanilla extract; whisk until well-combined.
Whisk in dry ingredients until combined.
Pour batter into prepared pan.
Bake for 45-55 minutes, or until a toothpick inserted into the center comes out clean.
Let loaf cool in pan for 10 minutes.
While loaf is cooling, whisk together sugar, lemon juice, and water.
Bring to a boil, whisking constantly.
Boil for 2-3 minutes, or until sugar has dissolved.
Remove to wire rack, and lightly brush syrup over warm bread.
Let bread cool to room temperature.
Whisk powdered sugar, 2 tablespoons milk, and lemon zest together.
Add in additional milk as needed to get thick but pourable consistency.
Pour over the top of cooled bread.
Let icing set before slicing.
Flour: Properly measuring the flour makes a huge difference in baked goods. To properly measure flour, either weigh it or stir/sift it to break it up. Lightly spoon it into the measuring cup and level.
Vegetable oil: Any neutral oil, like canola, will work.
Sour cream: I've used regular and low-fat sour cream in this recipe. Both have worked well. I don't recommend using fat-free sour cream.