[he follows, keeping his voice low, both to spare Garry's sensitive ears and keep them from being heard]

A metaphorical fire, as opposed to a literal one, refers to something troublesome - an argument, perhaps, or a missing crucial object. One might put out a metaphorical fire by attempting to keep the conversation civil, or perhaps giving one of the arguing parties different directions to the luncheon where the argument would have feasibly taken place, therefore keeping it from happening at all. They could also help to locate the missing object, or find a suitable replacement.