There's been some really good discussions on the subject, an especially cool theory was put forth here just recently.

Chances are Denna is a descendant of the Lockless family, but not a Lackless specifically. Most likely she is a "Lack-key". Caudicus told us a little about them:

“It’s generally accepted that there was some sort of falling out that splintered the family. Each piece took on a separate name. In Atur they became the Lack-key family.They were numerous, but fell on hard times. That’s where the word ‘lackey’ comes from, you know. All those paupered nobility forced to scrape and bow to make ends meet. In the south they became the Lacliths, who slowly spiraled into obscurity. The same with the Kaepcaen in Modeg. The largest piece of the family was here in Vintas, except Vintas didn’t exist back then.”

Denna being part of the Lack-key family explains her situation perfectly. The way Caudicus speaks of them in the past tense makes it clear that there aren't many of them left. Mirroring this, we know that Denna has no home nor any idea of where she came from. She's been struggling to get by since the first time we met her. The only thing she does have is her ring, which being covered in Yllish knots (just like the a certain box), is most likely an ancient Lockless heirloom.

Now whilst the Lack-key branch ended up penniless after the split, the Lackless branch enjoyed the opposite. Unlike their kin in the west, the eastern branch of the family stayed behind and consolidated their wealth and power. Even thousands of years later they're still important enough to be marrying the second most powerful man in Vintas.

Some other branches are also mentioned. The Lacliths, for example. We've actually met one of them. He was a woodsman whom stayed with Kvothe's troupe early in the first book. There's some interesting stuff regarding them as well, but I'll leave that for another post.

So, we have all these descendants spread out across the four-corners and we aren't really sure how it all fits together. Some of them have brown eyes, some of them have green eyes, some of them have blue eyes, some even have eyes that change colors. If that sounds a bit familar, here's a fun quote from early book one:

“The story’s older,” my mother explained. “It’s more like he’s looking at great-great-grandchildren.”

“And they’re scattered to the four corners,” my father groused. “And when I finally do find one, it’s got five eyes: two greens, a blue, a brown, and a chartreuse. Then the next one has only one eye, and it changes colors. How am I supposed to draw conclusions from that?”

I'm not sure how much we can gleam from the eye colors though. The Lackless/Lack-key seem to have either brown or green eyes. Lochees/Laclith I've no idea. Chronicler seems like he might be related to Skarpi and Skarpi has blue eyes, but I can't recall if it's ever mentioned what color the Chronicler's eyes actually are.

The last two however, "only one eye" and an eye that "changes color" fit perfectly with two ancient figures from the old legends. Namely, Selitos One-Eye for obvious reasons and Iax "the shaper of dark and changing eye". Could Selitos and Iax have been Lockless brothers? Was the creation war what drove the family apart? Did Kvothe inherit his naming prowess and changing eyes from Selitos and Iax themselves?

There's not all that much to go on from just eye colors though. An alternative interesting thing to look at is the names themselves, as Caudicus told us:

“You see, names can tell you a great deal about a thing.”

First off there's the Lackless. They're wealthy, powerful, influential. They literally lack nothing. They're Lack-less. When the family split apart they stayed behind and kept the most famous family heirloom, the "Lockless Box".

Next there's the Lack-key. They're penniless, homeless, disjointed. They literally lack everything. Their key characteristic is their Lack. The Lack-key. The only thing they have left from the original family is the heirloom ring that Denna is in possession of.

So, why are these two names and heirlooms important? Well, we know both artifacts have Yllish knots written on them and to compound on that we have hints of a type of magic that involves writing, as seen here:

Denna looked embarrassed as she asked, “What if someone told you they knew a type of magic that did more than that? A magic where you sort of wrote things down, and whatever you wrote became true?

What if, when the family split up, they each took a piece of a whole, breaking apart a name, and thats how they got their individual namesakes.

For the Lack-key family, the ones whom lack everything, they have a ring with the name "Lack". Denna literally is walking around with a magic ring that makes her lacking. It's so bad she can't even keep it on her finger without fidgeting with it nonstop. Even though men shower her with fancy things, in the end she always ends up lacking. Ambrose had the ring only for a short time and ended up having his whole room burned up. Denna keeping it all these years explains why she has nothing despite being exceptionally talented.

On the other side of the coin we have the Lackless family, whom have everything, whom are lack-less. I guess if you have magic that comes true when written, naming yourself Lack-less is a great idea. The problem here is that for their box to be the "Lockless Box" they need the "less"! Lacking "less" means they instead are stuck with just a "Lock Box". They only have half the name and thus, much to their dismay, the box remains locked.

It seems likely that this is how the box will finally be opened. Kvothe being the Lackless heir will bring the "Lock" box and Denna being the Lack-key heir will bring the key, "Less". Thus with the name restored box will become "Lockless". It's important to note that this might be a very bad thing. If someone went through such trouble to create a Lockbox that cannot be opened, there's a good chance that what's inside might be very dangerous.

But what exactly is inside? The popular theory around here is that inside the box is the stone that Selitos used to put out his eye. Kvothe's guessed that the object inside was "made of glass or stone", which fits perfectly with the "shard of mountain-glass" that Selitos used for said gouging. The theory states that someone used the stone, or more specifically the blood that covered it, to sympathetically bind it to Selitos. Then from there they shaped a "Lockless Box" out of a specific type of wood and inside this box they put the blood covered mountain-glass. In doing so they bound Selitos to the tree the box was made from. To be sure that his entrapment was permanent they then reshaped the "Lockless Box", taking away the "Less" and leaving it as "Lock Box". A box specifically shaped to have no lock, no way of opening, a permanent prison for the Cthaeh.

In a box, no lid or locks. Lackless keeps her husband’s rocks.