Cream sugar and butter until creamy. Gradually stir in egg yolks. Mix flour and baking powder together and fold into batter. Add lemon zest and rum.
Beat egg whites until stiff and fold into batter along with ground nuts.
Grease baking dish with butter and sprinkle with breadcrumbs. Pour in batter and smooth. Bake in a preheated oven at 180°C (approximately 350°F) for 80 minutes. Remove, cool slightly and remove from dish.
Mix powdered sugar with lemon juice until thick and spread over cake.
Decoratively top with walnuts. Slice and serve.