Preheat the oven to 350°F Grease 2 - 9 inch round cake pans and line the bottom of each with a disk of wax paper (see recipe #452719).
Sift the flour with the baking powder and salt.
In a large mixing bowl, cream the butter with the sugars until light and fluffy. Beat in the eggs, one at a time. Stir in the lemon zest.
In a small bowl mix the mashed bananas with the vanilla and milk. Add the banana mixture and the dry ingredients to the butter mixture alternately in 2 or 3 batches and stir until just blended. Fold in the nuts.
Divide the batter between the cake pans and spread it out evenly. Bake until a cake tester inserted in the centre comes out clean, 30-35 minutes. Let stand 5 minutes before unmolding onto a wire rack. Peel off the wax paper.
For the frosting, cream the butter until smooth, then gradually beat in the sugar. Stir in the lemon zest and enough juice to make a spreadable consistency.
Set one of the cake layers on a serving plate. Cover with about one third of the frosting. Top with the second cake layer. Spread the remaining frosting evenly over the top & sides of cake.