Lightly butter the insides of 4 (1-cup) ramekins, then dust with sugar. Space them evenly on a baking sheet and put in the freezer.
Put the bananas, brown sugar, lemon juice, and rum in a medium saucepan. Cook uncovered, over medium heat, stirring occasionally, until the bananas begin to soften, about 7 minutes. Mash the bananas with a potato masher or large fork until mostly smooth; continue cooking to make a thick puree, about 8 more minutes. Cool to room temperature.
Position the oven rack in the lower third of the oven and preheat to 425 degrees F.
Whip the egg whites and salt in a large bowl with an electric mixer at medium-high speed until foamy. Increase the speed to high, gradually pour in the 2 tablespoons sugar, and whip until the whites hold soft peaks. Fold a quarter of the whites into the banana mixture and then fold in the remaining whites. (Don't dally here; timing is everything with souffles. Whip, fold, and get the souffle in the oven without missing a beat.)
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