Preheat oven to 375°F. Make topping: Melt butter over medium-high heat in a 10- or 12-inch ovenproof skillet at least 2 inches deep. Stir in brown sugar and cook, stirring often, until smooth, about 1 minute. Add lemon juice; stir until bubbling, about 1 minute. Arrange bananas in a flat layer over bottom of pan and cook until softened, about 2 minutes. Sprinkle coconut on top; remove from heat.
Make cake: Mix flour, baking powder and salt. With an electric mixer, beat butter on high speed until creamy, about 3 minutes. Add sugar; beat until light and fluffy, about 5 minutes. Reduce speed and add eggs, one at a time, beating well after each. Beat in vanilla. Alternate adding flour mixture and milk, starting and ending with flour.
Pour batter over bananas and coconut; spread evenly. Be careful not to mix bananas and coconut into batter.
Bake until cake springs back slightly when touched in center, 30 to 40 minutes. Let cake sit in skillet for 5 minutes to allow juices to blend into cake. Run a knife around outside of cake to loosen, then carefully invert onto a wire rack to cool. Serve warm or at room temperature, with ice cream or whipped cream, if desired.