Beat eggs with sugar until frothy. Also stir the butter until frothy, add the egg mixture and lemon zest. Mix the flour with baking powder and sift into the batter. Mix by hand.
Grease a loaf pan, pour in the dough and bake for about 55 minutes.
In the meantime, cook the syrup from the orange and lemon juice and the powdered sugar.
Take the cake out of the oven, immediately poke as many vertical holes as possible with a thin knitting needle, pour in the syrup evenly. Let the cake cool down.
Make a thick icing from powdered sugar and lemon juice and brush the cake with it.