[Kent2010]

Houses of lamentation is a very poetic expression, not something I would have expected from Witchie. maybe he shares some of Saruman's eloquence.
-Bethberry

I think that is the purpose, whether the Houses of Lamentation are physically a place or not, there is intense imagery and lots of word play.

A lament is a poem/song that expresses the grief or mourning of loss - there is a lament to Gandalf in LOTR. Also, Beowulf, The Iliad and The Odyssey have lamental elements. You have laments in the Hindu Vedas, the Sumerians city lament about Ur - it is one of the oldest and widespread writing styles.

But I might be getting off track, what I notice is the word play all revolving around "The Houses of lamentation."

I guess his place would have been in the Houses of Lamentation, if not at the foot of Sauron's throne.
-Gordis

Considering what Frodo finds out in Rivendell about his wound, it is I think a good observation:

You would have became a wraith under the dominion of the Dark Lord; and he would have tormented you for trying to keep his Ring, if any greater torment were possible than being robbed of it and seeing it on his hand.'

There might be two different types of torment here - the physical torment that would be inflicted by Sauron, on Frodo, for taking the Ring. But then the other kind of torment that would be "greater" Frodo's loss of the ring and seeing another have it. You might call it "Frodo's lament of the Ring," not just losing something so precious and desirable, but knowing someone else has it and you can't get it.

Thinking of this route, I wonder if Gollum was tormented not just in the dungeons of Barad-dur, but the Houses of lamentation. Didn't Gandalf say Gollum was getting better that he was healing? But he is captured by Sauron and is filled with a renewed lust to find the Ring and get it back. Then Gollum going through his own "lament of the Ring," not just grief for losing it, but the grief in knowing who has it and you can't get it back. Although Gollum does scheme to get it back, because he has the opportunity. Frodo would not have this opportunity if the Morgul knife was able to finish its job.

I wonder if there is an actual physical "Houses of lamentation" or not, and there is no way I can answer that, but it seems more of a mental state. Being "taken" to the Houses of lamentation does not necessarily mean there is a physical place, it could be imagery. But there is definitely a severe torment connected to the HoL (I am paraphrasing now, because my finger are getting tired ). The reason I question if it is an actual place is because of the torment that Frodo would undergo when being taken to Sauron's throne, and it is a torment that would be greater than any physical torture Frodo would undergo. It could be similar to the torment Gollum undergoes, being Frodo's guide, but knowing he has his precious.

"Houses of lamentation" could be a mental state, that the Nazgul (and Sauron) have the ability to inflict on people. Placing their victims in an almost permanent state of mental torture through loss, grief, and mourning. It is healthy to mourn, but a permanent state?...not good. And being taken away to the HoL is more poetic imagery of the permanent state of mourning the Nazgul have the ability to inflict on people. I think it is the very state and torment the Nazgul go through as well, so I wonder if the Nazgul can inflict the torment that they themselves go through?

With Gorbag's quote...

...And they skin the body off you as soon as look at you...

I don't interpret this as being able to skin somebody, but more as a terrifying description of the Nazgul, and why people should be terrified of them. That is these guys all backlashed to their mother's repeated attempts to make her boys more social - they don't ask questions, they don't make friends, they would much rather torture somebody.