Cut the bananas in half crosswise then into 3 slices lengthwise, making 12 slices in all.Place 4 tablespoons sugar onto a plate.  Coat the bread slices with the sugar.  Lightly press 2 slices banana onto each bread slice.Heat 4 tablespoons butter in a 12-inch skillet over medium heat.  Add the sandwiches in batches, banana-side down, and cook for 5 minutes or until the sugar is caramelized, turning the sandwiches over carefully once halfway through cooking.  Remove the sandwiches from the skillet and keep warm.Stir the remaining sugar, butter and the lime juice in the skillet. Cook and stir until the mixture boils and thickens.  Top the sandwiches with the ice cream and drizzle with the sauce.