For Lemon Syrup
Preheat your oven to 350 degrees F. Mix together the flour, salt, and baking powder in a small bowl. Set aside. In a medium-sized bowl, mix together the oil, one cup of sugar, eggs, zest, and milk until well combined. Add the dry ingredients all at once, mixing with a spoon to combine well.
Pour the batter into a greased loaf pan. Bake on the center rack of your oven for 45 minutes, or until a toothpick inserted in the center comes out cleanly. Cool for ten minutes in the pan, then remove to a baking rack. Mix together the juice from the lemon and 1/2 cup of granulated sugar to make a lemon syrup. Poke the top of the lemon bread all over with a thin skewer and brush the lemon syrup all over the bread. Cool completely on the rack.
When the lemon bread has cooled, mix together the confectioners sugar and lemon juice to form a thick glaze. Add a teaspoon of lemon juice at a time. You want the glaze to be thick so it will hold its shape when you drizzle it over your bread. Pour the glaze into a small plastic bag (like a sandwich bag), clip the corner, and drizzle the lemon glaze over the bread.
I like to wrap the bread in plastic wrap after the glaze has set and chill the bread in the refrigerator overnight. This gives the bread time for the syrup to permeate the bread and allows the flavors to develop fully.