Preheat oven to 350 F and line a loaf pan with parchment paper.
Combine the lemon zest and sugar in a large mixing bowl. Using your hands, rub the two together to release the lemon aromas and "mix" together.
Pour in the melted butter and mix together. Then add vanill and the room temperature eggs one at a time, mixing in between.
Add in the milk, sour cream, and freshly squeezed lemon juice, then mix.
Toss in the flour, baking powder, and salt and continue mixing until just smooth. Try not to overmix the cake batter.
Transfer the lemon loaf cake batter into the parchment lined loaf pan and then bake for 45 minutes or to 1 hour. Check at 45 minutes!
Once loaf is cooling down, combine the icing ingredients and mix with a whisk until smooth and pourable. If it's too thick, add in 1 teaspoon of milk or cream to loosen it up so you can pour it.
When the loaf cake is completely cool, pour the icing over the entire top and let it drip down over all the edges.