Heat oil in a deep fryer or large saucepan to 350 degrees F (175 degrees C).

Place brown sugar in a shallow bowl. Roll each banana quarter in brown sugar until coated. Wrap a lumpia wrapper around each coated banana, sealing the last edge to the roll using a spoon or your finger dipped in water. Repeat with remaining bananas and wrappers.

Working in batches, fry lumpia in hot oil until golden brown, about 5 minutes. Transfer cooked lumpia to a paper towel-lined plate using a slotted spoon. Some sugar may leak out the sides of the lumpia while cooling.