Squeeze the lemon juice over the bananas. Melt the brown sugar and butter in a medium skillet over medium-high heat. Place the bananas in the skillet cut-side down and saute, flipping carefully once color has developed on one side. Sprinkle the cinnamon over the bananas.
Remove the skillet from the heat and add the rum. Carefully ignite with the flame from the stove or a match. As the flames begin to subside, carefully spoon the sauce over the bananas.
Prepare 4 serving dishes with a large scoop of vanilla ice cream. Top with a banana slice and generously spoon the sauce on top. Serve right away.