Wow, now this thread got me thinking. This will just be my speculation, but I got excited by the idea:
We've been given the information that Yordles live extremely long in the new lore, even though they probably had human-like lifespan in the original lore.
Poppy is alive since the founding of Demacia, even perhaps a bit longer than that. And it looks like it is emphasized that it's very important for her to have a purpose. A Yordle without a purpose is a catastrophe. Maybe they are capable of incredibly long lifespans as long as they have purpose? It's also said that Yordles have some kind of innate magic. Who knows, maybe they were magically altered species, for all we know. By who knows whom or how. Maybe a strange spaceship fell from the sky and gave them sentience alongside magic, if Riot decides to keep the Mothership from the Old Lore (pls Rito it's an epic part of lore).
Also, Mordekaiser has been shown to have had his last, I note, last reign, how long ago? A thousand years ago? Before he was taken down and his infamous skull-fortress seized. These are all elements of introduction. What if...
A thousand years ago, Mordekaiser finally fell. The army that took over the skull-fortress would found Noxus in the future within that very stronghold. But when they explored what they had just conquered, in the ~~basement ~~ dungeon they found a small creature, covered in black fur. But nobody dared approach it, there was a sense of ominous evil surrounding it. We now know that was Veigar they found, locked away during Mordekaiser's rule (as you suggested). He's perhaps, 1500 years old? Maybe even 2000? All those years spent chained up in darkness, but he did have a purpose. To escape and take revenge on the entire world. All of his hatred boiled inside him while he was locked away. But I find this to be very similar to Xerath's story. I still can't compare Veigar's and Xerath's timeline, for that we would need a relation between Shurima and Mordekaiser's rule. Have the ancient heroes of Shurima ascended to fight against the Watchers, or Mordekaiser? Anyway, it could be possible to create a difference between Xerath and Veigar this way: Xerath's primary goal, revenge, was kind of fulfilled. The empire that enslaved him was destroyed. Now he seeks to be free and achieve the supreme power. Veigar on the other hand, is free now, but his search is not a search for power for its own sake as it is for Xerath, but rather for achieving his goal, and that's revenge for all those years spent locked. They both have what the other one is searching for.
For Yordle company and sanity, I believe that can still be kept. Maybe Poppy's a bit different from other Yordles, and so she only needs purpose to stay sane. So maybe it's a combo of companionship + purpose that keeps Yordles alive and sane. Veigar on the other hand, had no empathy from his kind, but he definitely had purpose. Alas, that purpose got twisted during all that time and he ended up the way he did. Maybe even sunlight plays a factor in their mental health?
Now, what if Demacia was founded in response to the foundation of Noxus? That they didn't just randomly come to be at the same time, and for some reason started to clash. In Poppy's new lore we're told that those caravans of people were heading for a place where they could found a nation of just - perhaps in contrast to Noxus. That implies that they already knew of a nation, which they disliked.
This would mean that, even though Poppy is old - she's definitely younger than Veigar. Now I wonder how old Lulu is. Perhaps she's older than Veigar?
imprisons 
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