Make the cake: Preheat the oven to 350 degrees F. Line the bottoms of three 8-inch round ungreased cake pans with parchment paper. Sift the flour, 1 cup superfine sugar, the baking powder and salt into a large bowl. Whisk the oil, 1/2 cup cold water, the egg yolks, lemon zest and 2 teaspoons lemon juice in a medium bowl until well combined. Make a well in the center of the flour mixture and pour in the oil mixture; stir with a rubber spatula until smooth. Set aside.
Beat the egg whites and the remaining 1 teaspoon lemon juice in a large bowl with a mixer on medium speed until foamy, about 1 minute. Gradually beat in the remaining 1/3 cup superfine sugar; continue beating until stiff peaks form, 3 to 4 minutes. Fold about one-third of the beaten egg whites into the batter with a rubber spatula, then fold in the rest until just combined.
Divide the batter among the prepared pans and smooth evenly. Bake until the centers spring back when gently pressed, 30 to 35 minutes. Transfer the cakes to a rack and let cool completely in the pans.
Meanwhile, make the frosting: Puree the strawberries in a food processor until smooth; strain through a fine-mesh sieve, pressing on the solids with a rubber spatula. Beat the marshmallow cream in a large bowl with a mixer on medium speed until smooth. Beat in the butter, 1 tablespoon at a time, until incorporated, then beat in the strawberry puree. Reduce the mixer speed to low; gradually beat in the confectioners' sugar until combined.
Assemble the cake: Run a knife around the edges of the cakes and invert onto the rack; remove the parchment. Put 1 cake layer on a cake stand or serving plate. Spread with about 1/3 cup frosting. Top with another cake layer; spread with another 1/3 cup frosting. Top with the remaining cake layer, then cover the top and sides of the cake with the remaining frosting. Refrigerate until ready to serve.
Photograph by Con Poulos
Recipe courtesy of Rebecca Beale for Food Network Magazine