To make the Banana Base: in a medium saucepan, over a high heat, brown the butter. Add the sugars and continue to cook stirring constantly until caramel color, about 5 minutes. Add the chopped bananas and stir until well coated. Continue to cook for 2 minutes. Remove from heat and stir in the dark rum and lemon juice. Transfer mixture to a food processor and pulse until smooth. Transfer to a bowl and allow to cool to room temperature.
Preheat the oven to 375 degrees F.
Brush the inside of 6 (6-ounce) ramekins with softened butter and dust with sugar.
To make the souffle: beat the egg whites on medium speed, in a mixer with the whip attachment, to soft peaks. With the motor running, add the sugar in a slow but steady stream. Continue to whip to medium stiff peaks. With a large rubber spatula, fold 1/2 of the meringue into the Banana Base. Add the finely chopped chocolate chips and fold in the remaining 1/2 of the meringue. Fill each prepared ramekin over the top with the souffle mixture. Bake the souffles for 12 minutes. Serve immediately.