Preheat oven to 350°F. Butter the bottoms and sides of two 8-inch cake pans and line the bottoms with parchment paper. Smooth papers down so they hug the bottoms of the pans.
In a medium bowl, combine dry ingredients: flour, cornmeal, baking powder, baking soda, and salt. Set aside.
In a large bowl, combine wet ingredients: sugar, 1 heaping tablespoon lemon zest, yogurt, vegetable oil, eggs, and 3 tablespoons of the lemon juice and whisk until smooth and combined.
Sift ⅓ of the dry ingredients into the wet ingredients and fold in using a spatula until just combined. Do the same with remaining ⅔ dry ingredients. Be sure not to overmix; fold only until no floury clumps remain. Divide batter evenly between prepared pans and smooth so it reaches the walls of the pan.
Bake cakes on the oven’s middle rack for about 30 minutes. The cakes are done when the surface looks golden brown and they have begun to shrink from the walls of the pan. Make sure the surface springs back when touched lightly and a cake tester comes out clean.
While the cakes are baking, reserve 1 tablespoon lemon juice to use on the strawberries and combine the remaining ½–¾ cup lemon juice with ¼ cup sugar. As you remove the cakes from the oven, immediately spoon the lemon-sugar mixture over the entire surface of each still-warm cake.
Set cakes on a rack to cool in their pans for around 20 minutes. When cakes are cool to the touch, run an offset spatula along the inner wall of the pans, and turn out the cakes on the rack to finish cooling.
In a medium bowl, combine the sliced strawberries with ¼ cup sugar and the reserved 1 tablespoon lemon juice. Let sit for 15 minutes until syrupy.
Place one cake layer on a serving plate. Spoon an even layer of berries (along with a little of their syrup) over top.
In a medium bowl, whisk the cold heavy cream together with the remaining 1 teaspoon lemon zest and 1 teaspoon vanilla (optional). Using a hand-held mixer, beat until cream has almost reached the stiff peaks stage, making sure not to over beat.
To finish assembly, add a layer of whipped cream atop the already layered strawberries, then add the second layer of cake. Top with remaining whipped cream and remaining berries. Serve immediately.