Preheat the oven to 350°F /175°C and grease and line 3, 6-inch cake pans or 2, 8-inch cake pans. I used 6-inch cake pans.
Add 2 cups of granulated sugar and 3 Tbsp fresh lemon zest into the bowl of a stand mixer or a large bowl. Massage the sugar and zest together with your fingertips to release the oil in the zest.
Add 2 cups + 2 Tbsp all-purpose flour, 1 1/2 tsp baking powder, and 1/2 tsp salt into the lemon sugar. Use a stand mixer with a paddle attachment or a hand mixer to mix on a low speed until combined.
Mix in 2/3 cup (1 & 1/3 sticks) unsalted butter slowly into the dry mix, on a medium-low speed. Continue to mix until no large chunks of butter remain and the mixture becomes crumbly.
Pour in 2/3 cup or about 5 egg whites and mix on low until just incorporated. The batter will be super thick at this point.
Mix in 1 cup of sour cream, 1 Tbsp vegetable oil, and 1 tsp vanilla extract. Scrape the sides and bottom of the bowl as needed with a rubber spatula.
Divide batter evenly between the prepared cake pans. If desired, top the batter with 1/2 cup fresh quartered raspberries, spacing them evenly across the pans. Press them into the batter a bit so that you don't end up removing all of them if you level the cake layers. Avoid using frozen or overly soft raspberries in the cake layers because they can create soggy, undercooked spots.
Bake 6-inch cake layers for 30-34 minutes, or 8-inch cake layers for 34-36 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs. Let the pans cool for 10 minutes, then run a small offset spatula around the perimeter of the pan to separate the cake from the pan.
Place cake layers into the freezer for 30 minutes to accelerate the cooling process. Once the layers are fully cooled, carefully flip the pans and remove the layers.
Use a serrated knife to level the tops of the layers right before you plan to assemble your cake. If you're making these in advance, wrap them tightly in plastic wrap and store them in the freezer.