Preheat the oven to 350°F. Grease and line a Grease and line a 9" x 5" (1 lb.) loaf pan with parchment paper.
Sift together the flour, cornstarch, baking powder, baking soda, and salt.
In a separate large bowl, combine the dairy-free yogurt, sugar, oil, lemon juice, lemon zest and vanilla. Add the dry ingredients to the wet ingredients, and mix together until just combined. Be careful not to overmix, it is ok if the batter is not perfectly smooth.
Transfer the batter to the lined loaf pan. If using a smaller loaf pan, add a little less batter, so that it only fills the pan ¾ full. Bake for 45-50 minutes, or until golden brown, and a cake tester/skewer comes out clean. Allow to fully cool in the pan.
For the glaze: sift the powdered sugar into a bowl. Add the lemon juice and whisk until smooth.
Transfer the cake out of the pan, and drizzle with the glaze. Slice and serve. Cake lasts for 3-4 days covered at room temperature.