Preheat the oven to 350 degrees F. Grease and flour a 8 x 4 loaf pan, then line it with parchment paper.
Cream the butter and 3/4 cup granulated sugar in the bowl of an electric mixer fitted with the paddle attachment, until light and fluffy, about 5 minutes. With the mixer on medium speed, add the eggs, 1 at a time, and the lemon zest.
Sift together the flour, baking powder, baking soda, and salt in a bowl. In another bowl, combine 2 Tbsp lemon juice, the buttermilk, and vanilla. Add the flour and buttermilk mixtures alternately to the batter, beginning and ending with the flour. Dump the batter into the prepared loaf pan, smooth the top, and bake for 45 minutes to 1 hour, until a cake tester comes out clean.
Combine 1/4 cup granulated sugar with 1/4 cup lemon juice in a small saucepan and cook over low heat until the sugar dissolves. When the cakes are done, allow to cool for 10 minutes. Remove the cake from the pan and set on a rack over a sheet pan; spoon the lemon syrup over them. Allow the cake to cool completely.
For the glaze, combine the confectioners' sugar and 2 Tbsp lemon juice in a bowl, mixing with a wire whisk until smooth. Pour over the tops of the cakes and allow the glaze to drizzle down the sides.