Kindred is perhaps the most metaphorical champion in the game, alongside Tahm Kench
First off, Kindred may not even exist, and may instead be an expression for death manifested in folklore and tales. This is supported by the unusual narrative and structure of her bio and stories compared to other champions.
Secondly, if Kindred does exist, they exist as a force of nature that represents the beliefs of death, given form by thought (presumably). This is up for debate, as much of Kindred is left open for elaboration.
Kindred was also one of the first champions to have their lore be "current" so to speak, and came out around the time League was suffering from it's 3rd (and current) overhaul. As a result her bio and stories, like that of other champs changed around this time, are somewhat short. Thus, there's not a lot to go on beyond guessing.
Here is what we know.
Lamb and Wolf are not two separate beings. Think one brain, two bodies. Even if they represent two halves of a whole, Kindred is essentially talking to itself.
Should the masks of Kindred ever be removed for whatever reason, something bad on a level that nobody can possibly comprehend will happen.
Lamb and Wolf are not immortal, and they seem to be linked to the belief of death via lifespan. Thus presumably, when all else is gone, Kindred will "hunt" itself.
There seems to be some limitation on Kindred's actual powers and abilities, which seem to be linked to what folk believe it can actually do.
The act of hunting seems to be mostly metaphorical, and it isn't known if Kindred actually plays a role in the death of the person, as seen in one of her stories. Everyone will meet Kindred at some point in their lives, which points to the fact that they are not attuned by time or logic, but rather that individual's "time". It also may point to the fact that Kindred is only visible to the victim at their "time" so to speak. This also hints more to the story of Magga being a folk tale and gives evidence that Kindred may not actually exist, or exist on a structural, narrative level where it is confined by general belief on its roles as to what it can do.
It is not known if Kindred has any actual power, though they are stated to dislike Karthus greatly due to his twisting of their nature. Despite this, it has not acted against Karthus or any members of the Shadow Isles, further lending credence that it either does not exist, or cannot act in such a manner beyond what it is allowed.
If the idea of Kindred being just a metaphor is true, then Kindred does not exist.
If Kindred does exist, then it seems to be restricted to the beliefs of Runeterra, and was seemingly born of these beliefs.
The final piece is the mystery of the lonely man, who supposedly split himself in two with an axe and became Kindred. It is my interpretation that this individual was the original Death of Runeterra, who fulfilled much the same function but desired a companion to speak to, even if that was itself. Or, it may simply be part of the story.
This is all that I have gathered about Kindred, who is most certainly one of the more enigmatic characters. The other one, Tahm Kench, is even more of a guesswork.
