Preheat oven to 375 for glass or light metal pan; 350 for dark metal or coated pan. Position a rack in the middle of the oven.
Grease and flour a 9x13" pan.
Put 1 tablespoon lemon juice in a measuring cup and fill with milk to the 2/3 cup line. Set aside.
Mash bananas with a fork, adding the remaining tablespoon of lemon juice to them as you mash. Set aside.
Combine cake mix and baking soda in a large mixer bowl and stir. Add bananas, softened butter, lemon-milk mixture, eggs, and vanilla. Beat at low speed about 30 seconds until moistened. Turn speed to medium and beat another 4 minutes.
Pour batter into prepared pan and place in oven.
For glass or metal pan, bake at 375 degrees for 28 to 33 minutes. For dark metal or coated pan, bake at 350 degrees for 31 to 33 minutes. Cake should be pulling away slightly from edges of pan when done, and the center should spring back when lightly touched with finger. Check for doneness at lowest time, but don't move cake in oven before then as it may fall.
Cool in pan on wire rack, then frost.
Spread chopped pecans on a baking sheet and bake in 375 degree oven for 5 to 8 minutes until lightly browned. Watch carefully to avoid overcooking! Set aside while you prepare frosting.
Have all frosting ingredients ready so you can move quickly while making the frosting, or it may set up before you can smooth it on the cake.
In a small saucepan, thoroughly mix brown sugar and flour. Add butter and milk, and set over medium-high heat until mixture comes to a rolling boil. Boil exactly 1 1/2 minutes.
Remove from heat; cool 5 minutes. Beat briefly with a wooden spoon until it begins to thicken. Mix in vanilla and continue beating until frosting is the consistency of thick honey, no more than 1 to 2 minutes.
Immediately pour frosting onto cooled cake and quickly spread with the back of a warm spoon before frosting begins to set up. Quickly sprinkle with toasted pecans.
You can serve immediately; although frosting may take several hours to completely set.