Line two 8 inch cake pans with a circle of parchment paper. Grease the sides with a little oil.
Preheat oven to 350°F (176°C) and position the racks so that the cakes will sit in the middle.
Combine the egg whites and salt in a large bowl or stand mixer, then whip to stiff peaks. Set aside.
Combine the olive oil, lemon juice, vanilla, and sugar. Whip/whisk for about 2 minutes, or until thick and somewhat foamy/airy.
Whisk flour, baking powder, and lemon zest together.
Using the paddle attachment of a stand mixer (or hand beaters) at low speed, gently mix approximately 1/3 of the flour mixture into the whipped oil and sugar. Add 1/3 of the ice water, and continue to mix. Repeat with remaining flour and water, stopping when the ingredients are just barely mixed. The resulting batter should be fairly thick, but still liquid enough to pour.
Gently fold the whipped egg whites by hand into the batter mixture, a little at a time. Work gently to avoid deflating the mixture.
Pour the batter into the prepared pans. Bake for 45-50 minutes, or until a cake tester comes out clean. Cool for 10 minutes, then gently invert the cakes onto cooling racks and set them aside.
Once the cakes have cooled, trim the tops (and sides, if you like) so they're flat. Cover one layer of the cake with the finished/cooled curd, then top with the second layer and more curd. Cover and chill for 1 hour, then serve.