Preheat oven to 350 degrees F. Grease an 8 1/2 by 4 1/2 by 2 1/2 inch loaf pan.
Combine flour, baking powder and salt in a bowl. set aside.
In a separate bowl, whisk together yogurt, 1 cup sugar, the eggs, and vanilla. Slowly whisk flour mixture into yogurt mixture. With rubber spatula, fold vegetable oil into the batter until well combined. Pour batter into greased pan and bake for about 50 minutes. To test: place toothpick or knife into center of cake, it should come out clean.
Allow cake to cool for 10 minutes in pan. Place dish towel underneath cooling rack. Carefully remove cake from pan and onto cooling rack. Poke cake 6 times with sharp knife. Indentations should be a few inches deep.
Cook remaining 1/3 cup sugar with 1/3 cup lemon juice in a small pan until sugar dissolves and mixture is clear. Pour over cake. Allow cake to cool for 10 minutes.
Mix together 1 cup confectioners' sugar and 2 tablespoons lemon juice and pour over cake. If you desire, double these ingredients to have a thicker glaze.