Beat sugar and shortening until smooth. Stir in milk and 1 teaspoon vanilla. In a bowl, whisk flour, baking soda, and 1/2 teaspoon salt; stir into sugar mixture. Mix in mashed banana, walnuts, and 1 teaspoon lemon juice. Spread into the prepared pan.

Bake until a toothpick comes out clean, 25-30 minutes. Cool in the pan on a wire rack.

For frosting: Beat confectioners' sugar, 1/2 banana, butter, 1 teaspoon vanilla, 1/2 teaspoon salt, and 1/4 teaspoon lemon juice until smooth. Spread over cooled bars and cut into squares.