ALL INGREDIENTS MUST BE AT ROOM TEMPERATURE
Preheat oven to 350 degrees F. Spray a 13 x 9-inch baking pan with non-stick spray.
Mix bananas with the 1 tbs lemon juice in a small bowl. Whisk in the eggs, milk and vanilla; set aside.
Place the flour, baking soda, salt and the sugars in a large bowl. Beat at low speed with electric mixer until combined, about 30 seconds.
Add the softened butter to the flour mixture and beat at low speed until combined, then beat at medium speed (high speed if using a hand mixer) for 2 minutes. Scrape down the sides of the bowl.
Add half the banana mixture and beat for 20 seconds, then add the remaining half and beat for 20 seconds.
Pour into prepared pan and place in the oven. TURN DOWN THE OVEN TEMPERATURE TO 300 DEGREES F.
Bake for 55-65 minutes (see NOTES) or until a toothpick inserted in the center comes out clean.
Cool completely.
Combine all frosting ingredients except the lemon juice, in a small bowl. Beat until smooth. Add only enough lemon juice to get a spreadable consistency. Frost top of cooled cake.