Considering that there are many movies that constitute the “Hellraiser” franchise, the lore and history surrounding the Lament Configuration is fairly robust. The most important feature of this demonic puzzle box is that once an individual solves it, it creates a pathway between this world and a dimension of untold pain and madness. The inhabitants of this evil realm are usually referred to as Cenobites, and although there is definitely a motif involving their general look — that is, they’re each frozen in various states of ecstatic physical torture — each Cenobite is unique, all of them generally twisted into a form of cruel mockery that represents their mortal failings in some way.
As mentioned earlier, the Lament Configuration often takes the form of an inconspicuous, yet mysterious, puzzle box that often becomes an obsession for the humans that gaze upon it. However, this shape — being a mystical object — is not fixed. Often, once a Lament Configuration is solved, the box has a tendency to unfurl, quickly changing size and appearance in a display of mechanical perfection.
The Lament Configuration that we’ve usually seen in the movies thus far, per the Hellraiser Wiki, was originally created by a French toymaker on the behest of a noble obsessed with magic in the 1700s. The noble thought this puzzle box would grant him untold powers with the ability to summon Cenobites for his own purposes, but it never works that way — indeed, summoning these entities tends to get you tortured and killed.
However, it is also important to note that this is not the first nor only Lament Configuration. In fact, in one of the prior “Hellraiser” movies, there are several on display.