Brush bananas with lemon juice. In a large skillet over medium-high heat, add butter and brown sugar, and stir until butter is melted.
Add bananas and saute until bananas are tender, about 5 to 8 minutes. Sprinkle cinnamon over bananas and remove the pan from heat.
Off the heat, add banana liquor (if using) and rum. Carefully ignite the pan using a long match. With a long-handled spoon, baste the bananas with the warm sauce until the flame burns out.
To serve, in each of four bowls add 1/2 cup of vanilla ice cream. Add one banana half and top with sauce. Serve immediately.
Notes
Bananas: Perfectly ripe and yellow or beginning to brown, ideally. (See below for tips about how to ripen your bunch.)
Banana liqueur: Look for this in the liquor store or online under this name or crème de banane. Again, skip it if you'd like this to be spiritless.
Dark rum: Also known as black rum, brands such as Bacardi, Gosling's, and Plantation are widely available. Simply omit for an alcohol-free option.
Vanilla ice cream: Or whipped cream, Greek yogurt, or another flavor of ice cream you prefer (like coconut)!