Preheat the oven to 350°F. Lightly grease six 4-ounce canning jars and place on a large rimmed baking sheet.
Begin by prepping the pudding ingredients. In a small bowl, mix together the sugar and lemon zest. Set aside. In a small stockpot, combine the lemon juice and water and bring to a boil. Once boiling, turn off the heat, but leave the pot on the burner.
To make the cake, combine the flour, cane sugar, and baking powder in a small bowl. In a larger bowl, whisk together the milk, vegetable oil, lemon zest, and vanilla to combine. Add the dry ingredients to the wet in two batches and mix until just combined.
Fill each of the jars halfway with the cake batter. Top the batter with 1½ teaspoons of the sugar-zest mixture. Pour 3 tablespoons of the water–lemon juice mixture on top of each jar. DO NOT COMBINE. It will look scary, but trust me.
Bake the cakes for 14 to 16 minutes, until the cake has risen and is golden and the lemon pudding is bubbling underneath and around the edges. Let the cakes cool on a wire rack for at least 15 minutes before serving.