Preheat oven to 350°F. Butter the bottom of an 8x8-inch baking dish. Line with parchment and butter the parchment. Do not butter the sides of the pan.
Place the egg whites in the mixer bowl fitted with the whisk attachment and start whipping on medium-low. Slowly add about 1/4 cup of sugar, then increase speed to high and whip until the whites have formed stiff peaks, about 3 minutes. Transfer to a large bowl.
Place egg yolks in the mixer bowl -- no need to clean -- and whip on high until thick and pale yellow, 5 minutes. Slowly add remaining sugar and continue to whip for another 2 minutes.
Add lemon juice and zest and beat in, about 1 minute.
Using a large spatula, fold egg white mixture into the egg yolk mixture in three additions.
Sift flour over the top and gently fold in.
Pour batter into prepared pan and bake 25-30 minutes, or until golden brown on top, cake springs back when pressed lightly, and a skewer inserted into the center comes out clean.
Let cake cool in pan for 15 minutes. Run a sharp knife around the edges and invert cake to remove from pan. Let cool completely.