Preheat the oven to 350 degrees F. Lightly grease a 9 x 13-inch pan.
In a large mixing bowl, whisk together the sugar, oil, lemon juice, lemon zest, applesauce, and vanilla until well combined. Add water and mix thoroughly.
Add the flour, baking soda, and salt, and stir until just combined. (Your batter may have a few small lumps and that's okay. You don't want to overmix.)
Fold in the poppy seeds.
Pour the batter into the pan. Bake for 35 minutes or until the edges are golden and begin to pull away from the pan. Take a toothpick, insert it into the middle of the cake and make sure it comes out clean. If it doesn’t bake in 5 minute increments until it does.
In the meantime, prepare your glaze by simply whisking together the powdered sugar and lemon juice. Start with 4 teaspoons, and if it’s too thick, add another one.
Allow the cake to cool completely (or at least 15 minutes if you just can't wait!) before drizzling with glaze. Enjoy!
Notes
Don’t overmix the batter: I know it seems odd not to make sure that cake batter is 100% smooth, but overmixed cake batter will have a weaker structure, leading to a fragile cake (which already has less structure as it’s egg-free). It can also impact texture, changing from fluffy and light to more chewy/gummy.
Measure flour carefully: I recommend using the spoon and level method. Spoon the flour into the measuring cup then the back of a knife to level it off. DON’T simply scoop the cup into your bag of flour all you’ll end up with too much flour and a denser cake.
Slicing the lemon sheet cake: This cake makes an excellent option for gatherings as there are so many ways to slice the cake - slice it into squares or bars of different sizes. You can even cut bite-sized pieces to be part of a dessert platter.