Preheat oven to 350 degrees Grease a 9 “ round cake pan and line the bottom with parchment paper.
In a small bowl, sift together flour, baking powder and salt.
In a large bowl whisk together yogurt, 1 cup sugar, eggs, lemon zest and vanilla. Whisk in the dry ingredients. Add the oil. Pour into prepared pan and bake for 45 minutes.
Meanwhile, heat juice from 2 lemons and 1/3 cup sugar in a small pan until sugar dissolves.
When cake is done, remove it from the pan onto a plate and pour the lemon mixture over the cake. Cool. Serve with vanilla ice cream or whipped cream.