Pour the sugar into a separate medium-sized mixing bowl. Grate all the zest from the lemons. Rub the zest into the sugar until the sugar is yellow and fragrant. Add the yogurt, eggs and vanilla to the sugar mixture. Whisk well, until the ingredients are combined.
In a medium mixing bowl, whisk together the flour, baking powder, and salt.
Preheat the oven to 350 degrees Fahrenheit. Generously butter and flour a 8½ by 4¼ by 2½-inch loaf pan.