Preheat oven to 350°. Grease and flour a 9 x 13 pan.
Place 1 ½ tablespoons lemon juice in a measuring cup. Top to 1 ½ cups with milk. Set aside.
Mix together mashed banana with 1 tablespoon lemon juice, set aside.
Beat together butter, brown, and granulated sugar until combined. Add in eggs one at a time and vanilla. Mix on high until light and fluffy. Combine flour, baking soda, and salt in a medium bowl. Alternate adding flour mixture and milk to egg mixture stirring just until combined. (Do not overmix). Fold in mashed bananas. Pour into greased pan. Put into the oven and reduce heat to 300 degrees. Bake 60 – 70 minutes (see note below) or just until a toothpick inserted in the center comes out clean (do not overbake). Remove from oven and place in the freezer for 45 minutes to make the cake extra moist. Cool completely before frosting.