The lemon base:
Combine all ingredients except butter in a saucepan.
Bring to a boil, stirring constantly with a whisk.
Remove from heat and add butter.
Pour the mixture into a baking dish that holds 2 liters/8 cups. Set aside.

The cake:
Preheat oven to 375 F (190 C).

Combine flour, baking powder, and salt. Set aside.

Beat egg whites until stiff, adding half of the sugar to have a very firm base. Set aside.

Mix the egg yolks, the remaining sugar, butter, oil, lemon zest, and lemon juice.
To this mixture, add the flour mixture, then add one-third of the meringue to thin the batter, and finally add the rest in two more additions.
Pour the cake batter over the lemon base and bake on the middle rack for 25 to 30 minutes or until a toothpick inserted into the center comes out clean and the top of the cake is golden.