Adjust the rack to the lower third, preheat your oven to 350°F (or 177°C), and grease your 8-inch loaf pan. For a slightly shorter loaf, use a 9-inch pan.
Whisk flour, salt, and baking powder in a bowl.
In a mixer, beat butter and sugar at high speed 'til creamy. Add eggs one by one, then mix in sour cream, lemon zest, lemon juice, and vanilla.
With your mixer at low speed, add the bowl of dry ingredients until combined. Avoid overmixing.
Spread this batter into your loaf pan. Bake for about 55 to 65 minutes (8-inch pan) or 45 to 60 minutes (9-inch pan), covering with foil after 25-30 minutes. Test for doneness with a toothpick.
Cool the cake in your pan on a rack for an hour, then flip it onto a plate to finish cooling.
For lemon icing, whisk the icing ingredients until smooth. Pour it over your cooled cake.