As stated in Fantastic Beasts and Where to Find Them (the book, not the movie), a lethifold is a creature that resembles a moving black blanket, something that looks like a creeping shadow when it hunts by night. It lives in the jungles of Southeast Asia and devours sleeping creatures, presumably going after mammals besides humans but known primarily for creeping into human bedrooms. 

Its main method of attack, assuming it has any other means, is to slither over a sleeping target and devour them. The only account recorded in English of surviving such an assault indicated that they are impervious to all spells but the Patronus, which chases them away as easily as it does dementors.

With that in mind, one wonders why they failed to appear in the main Harry Potter novels. They are, after all, an utterly terrifying concept, a creature which can raise the stakes merely by appearing, to a degree equalled only by Voldemort himself. Based on the above description, they are even more dangerous than dementors, because dementors can be commanded; there is no indication that lethifolds have the cognition necessary to even notice a command. All they do is sneak and devour.

So, from a Watsonian perspective, it may simply be that Voldemort could not possibly have controlled Lethifolds even if he wanted to. Nor even herd them into a box for safekeeping. He is not the sort of person who would cast a patronus, after all. 

From a Doylist perspective, the trouble with Lethifolds is that they are too scary. Putting them in the main Harry Potter books would have turned them from children's adventure novels into horror stories instantly. For a Lethifold may be said to be horror embodied, as Dementors are despair embodied. The key feature of a horror story is the lack of hope. When a Lethifold attacks, there is no hope -- 

Except by magically shoving it in their faces. No wonder a Patronus can chase away a Lethifold as easily as a Dementor! A patronus is hope embodied, and chases horror and despair away in equal measure. Harry Potter could have faced down a Lethifold by his fourth year of schooling, as long as he could see it coming. Everyone else had to wait until the next year to perfect their Patronuses, but eventually they would have been able to resist those creatures.

Which may be why they made no appearance -- as such creatures are described in a rather all-or-nothing fashion, they could either be implacable horrors in the early books or easily-foiled minions later on, never complex enough to pose a genuine challenge once their key weakness was discovered. As creatures go, Lethifolds appear to be rather one-note.

One might say they are flat characters.

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