Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x9-inch baking pan.
Beat sugar and shortening together in a large bowl until smooth. Stir in milk and 1 teaspoon vanilla. Whisk flour, baking soda, and ½ teaspoon salt together in a bowl; stir into sugar mixture. Stir in 1 banana, walnuts, and 1 teaspoon lemon juice. Spread evenly into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 25 to 30 minutes. Cool bars in the pan on a wire rack.
Beat confectioners' sugar, ½ banana, butter, 1 teaspoon vanilla, ½ teaspoon salt, and ¼ teaspoon lemon juice in a bowl with an electric mixer until smooth; spread over cooled bars, then cut into squares.
