1. To make the lemon pudding cake, zest your lemon and grease an 8 inch square baking pan or line the bottom with parchment paper. Set the zested lemon and pan aside.
2. Preheat the oven to 350° Fahrenheit (176° Celsius).
3. Whisk flour, half cup sugar, baking powder, baking soda, and salt in a large mixing bowl.
4. Stir in lemon zest, dairy free milk, melted plant based butter or oil, and applesauce until batter is just evenly mixed.
5. Spread cake batter into the prepared pan.
6. Stir water (not boiling), lemon juice, and remaining sugar in a measuring cup until sugar dissolves.
7. Pour this liquid evenly over the top of the cake batter. It will look very watery.
8. Bake on the center rack of the oven for 35 minutes. Remove and let cool.
9. You may eat the cake right away, but I recommend refrigerating at least 8 hours or overnight, because the pudding layer thickens considerably as it chills.
10. Store leftovers after a day in the refrigerator for up to 4 days. or freeze for up to 3 months.