1. Preparation: Begin by preheating your oven to 350°F (175°C). Grease and flour a 9 x 13-inch baking pan.
2. Lemon Milk Mixture: In a measuring cup, combine 1 ½ tablespoons of lemon juice with milk to make 1 ½ cups. Set this aside.
3. Banana Mixture: In a separate bowl, mix the mashed bananas with 1 tablespoon of lemon juice. Set this aside as well.
4. Creaming Butter and Sugars: In a mixing bowl, beat the softened butter, brown sugar, and white sugar until well combined. Add the eggs one at a time, followed by the vanilla extract. Beat on high until the mixture is light and fluffy, resembling the texture of frosting.
5. Dry Ingredients: In another bowl, whisk together the flour, baking soda, and salt.
6. Combining Mixtures: Alternately add the flour mixture and the milk mixture to the egg mixture, stirring just until combined. Remember, overmixing is a no-no. Gently fold in the banana mixture.
7. Baking the Cake: Pour the batter into the prepared pan. Place it in the oven, then immediately reduce the heat to 300°F (150°C). Bake for 60 to 70 minutes. A toothpick inserted into the center should come out clean. Be careful not to overbake.
8. Moisture Lock: After baking, place the cake in the freezer for 45 minutes. This trick helps to lock in moisture. Allow the cake to cool completely before frosting.

For the Frosting:

1. Creating the Frosting: In a bowl, cream together the butter and cream cheese until fluffy. Add in the lemon zest and juice.
2. Final Touch: Gradually add powdered sugar until you reach your desired consistency. Spread this luscious frosting over the cooled cake.