Preheat oven to 350° F. Grease and flour an 8-1/2x4-1/4x2-1/2-inch loaf pan. Line the bottom with parchment paper.
Use a fine grater to remove the peel from all four lemons. Set lemons aside.
In a medium bowl, combine 1 cup of sugar with the lemon zest. Use your fingers to rub the zest into the sugar.
In the bowl of a standing mixer fitted with the paddle attachment, cream the butter and lemon sugar until light and fluffy (about 5 minutes).
With the mixer on medium speed, add the eggs one at a time - blending well after each addition.
Sift together the flour, baking powder, baking soda, and salt in another bowl. Set aside.
Cut each of the four lemons in half and squeeze the juice into a small bowl, removing seeds as necessary. Set aside ½ tablespoon of lemon juice for the cream cheese icing.
In another small bowl combine ⅛ cup of the lemon juice, buttermilk, and vanilla.
Alternate adding flour and buttermilk mixtures to the standing mixer batter, beginning and ending with the flour.
Spread the batter into prepared loaf pan, smooth the top, and bake for 45-50 minutes, until a toothpick inserted in the center comes out clean and the edges have browned.
Combine ¼ cup granulated sugar with ¼ cup of lemon juice in a small saucepan and cook over low heat until sugar has dissolved. Set aside on stove top.
When the loaf is done baking, cool for 10 minutes on a baking rack. Slide a knife or icing spatula around the edges to loosen and remove loaf from pan.
Spoon the lemon syrup over the loaf as it continues to cool on baking rack.