Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x5-inch nonstick loaf pan and "flour" the pan with 2 1/2 tablespoons sugar, tilting so each surface of the pan is dusted with sugar. Discard any excess sugar.

Whisk together flour, cornstarch, and baking powder in a mixing bowl; set aside.

Place baking soda in the palm of your hand and wet with water to form a paste. Rub paste vigorously all over 1 lemon. Rinse lemon thoroughly, zest it, and place zest in a large bowl. Juice the lemon into a liquid measuring cup and add enough juice from remaining 2 lemons to measure 1/3 cup; add to lemon zest.

Add sugar, olive oil, and cream cheese to the lemon mixture. Mix thoroughly with an electric mixer until most of the sugar has dissolved. Whisk in eggs, applesauce, sour cream, and buttermilk until well combined. Whisk in 1/2 of the reserved flour mixture until incorporated. Whisk in remaining flour mixture until just combined. Immediately pour and scrape the batter into the prepared loaf pan. Place loaf pan, uncovered, on a baking sheet.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 42 to 45 minutes. Cool on a wire rack for 10 minutes. Run a table knife around the edges of the pan to loosen. Invert carefully onto a serving plate or cooling rack. Let cool for 30 minutes before serving, or cool completely to room temperature before wrapping and refrigerating.