Preheat your oven to 350°F (175°C).
In an 8x8 inch ungreased baking pan, whisk together the flour, sugar, baking soda, and salt.
Make three wells in the dry ingredients. Pour the vinegar in one, the vanilla in the second, and the oil in the third.
Sprinkle in the lemon juice and zest, then pour cold water over everything.
Mix it all together with a fork or spoon until well combined and smooth.
Bake for 30–35 minutes, or until a toothpick inserted in the center comes out clean.
Let the cake cool completely before slicing. Dust with powdered sugar or a simple lemon glaze if desired.