Peel and slice bananas diagonally ¼ inch thick.
Pour orange juice into a small shallow bowl.
Mix brown sugar and cinnamon in another bowl.
Melt 1 tablespoon butter in a 9-inch frying pan over medium heat.
Dip ⅓ of banana slices into orange juice and then into brown sugar mixture.
Add to pan and cook until slightly browned and glazed on both sides (about 1 minute total).
Spoon into 2 shallow dessert dishes. Repeat with remaining bananas.
When all are cooked, then add lime juice, remaining orange juice and brown sugar mixture to pan.
Cook over medium heat, stirring until boiling and syrupy.
Pour over bananas and top with sour cream.