Preheat the oven to 325 degrees F. Grease a 9X13-inch baking pan with cooking spray and set aside.
In a medium bowl, whisk together the flour, baking powder, baking soda and salt. Set aside.
In a large bowl, combine the lemon zest and sugar and lightly rub together with your fingers until well combined (this releases the oils in the zest and amplifies lemon flavor). Whisk in the eggs, oil, applesauce, yogurt, lemon juice and vanilla; mixing well.
Stir in the dry ingredients with a wooden spoon or spatula until just combined (don't overmix!).
Pour the batter into the prepared pan and bake for 25-35 minutes until a toothpick inserted in the center comes out clean or with moist crumbs.
While the cake is baking, whisk together the glaze ingredients until smooth and pourable (I use the full 2 tablespoons lemon juice but you might want to start with the lesser amount and add more, as needed, if you don't want your glaze quite as runny). Let the cake rest for 10 minutes after baking and then pour the glaze over the warm cake.
Serve warm, at room temperature or chilled. This cake, if well-covered, stays moist for several days.
Notes
Applesauce + Oil: if you don't have applesauce or don't want to use it, just up the oil amount to 3/4 cup instead of 1/2 (conversely, you could experiment adding more applesauce in place of the oil although I haven't tried it). Lemons: with the freshly squeezed lemon juice in the cake and in the glaze, you'll probably need about 4 large lemons for this recipe. Don't forget to zest them before you juice them! Zest: also, if you don't have a zester, you can use the small holes of a box grater to zest the lemon - just take care not shred too deep into the rind of the lemon (the white part is bitter!).