Mash bananas with a fork until creamy and pour into a large mixing bowl.
Add eggs, butter, shortening, and sugar, and mix until smooth. Then, add buttermilk.
Add salt, baking soda, vanilla, and lemon juice.
While stirring the batter, add flour one cup at a time until completely incorporated. It is a very "wet" cookie dough, so don't think you need to add more flour; it's ok the way it is.
Bake at 350°F (175°C) on an ungreased cookie sheet for 10-12 minutes or until slightly golden brown. Let cool for 30 minutes before frosting.
For the Frosting
Cream butter, vanilla, and salt in a medium-sized mixing bowl.
Add 2-3 cups of confectioners' sugar and mix.
Slowly add milk one teaspoon at a time until you get the desired consistency (it should not be runny or thick, somewhere in between so it will hold on the cookies).
Frost cookies with a knife and sprinkle with chopped walnuts or nuts of choice.
Notes
To STORE Banana Cookies, keep them in an airtight container at room temperature for up to 3 days. For longer storage, you can FREEZE the cookies for up to 3 months. Place them in a single layer on a baking sheet to freeze, then transfer to a freezer-safe container.To REHEAT, thaw at room temperature, and if you prefer warm cookies, heat them in the microwave for 10-15 seconds or in the oven at 300°F (150°C) for 5 minutes.