I just realized just WHAT Dr. Mundo is...
There are not many purple folks in this game, and as I can say with certainty that he is neither yordle nor fae, that leaves only one connection: Jax.
Now how does an Icathian baby, of a civilication that is said to have died out due to their void connection long before the fall of the Shuriman Empire, end up in the lowest levels of Zaun? That is like, several thousand milea and a few centuries to get past, absolutely impossible, especially for a baby, even if it was abnormally strong and seemingly immortal.
My theory is that this must have been a side effect of the fall of Icathia. The void is a plane beyond time and space, so being in there for a month without an anchor to your entrance point in reality, and then leaving again at a random point, could totally throw you into a different space and most importantly, a different time. And it would most likely make you insane. I think the fact that Mundo went through that as a baby saved him in some regard: you can't get insane when you don't understand anything by default and have neither a sense of object permanence nor a fully developed sentinence. Sure, it made him bonkers for years to come, that's for sure, but not in a way that Void-worshippers are (who I suspect to be like cults from lovecraftian literature - pretty fucking crazy)
So baby Mundo fell into the Void. Now, how did he get out again?
And this is where Zaun comes into play - and the lowest levels of it, where all random toxical spill and refuse gathers to form who knows what. Twitch came from it. Zac's entire existence is thanks to that. And it wouldn't have been so weird if some shit just came together in a REALLY wrong way and opened a temporary Void portal - a portal so absolutely disgusting no Voidborn would even WANT to cross it, but whgen talking about little kids there is one thing you can sure of: take your eyes of them for one darn second and they are about to put the most disgusting thing into their mouth they gonna get their tiny hands on - bonus points if it could potentially kill or injure them. So we have baby Mundo in the void, the disgusting portal opens for only a really short time before it falls apart again, and it doesn't even take long and he crawls into it and ends up in Zaun.
And the rest of the lore is what we could read now.
However, I doubt that his powers are Void-related and more of a Icathian thing. For a long time their civilication and their power was build on the Void, so I guess they bargained some powers out for their people, even if it meant their doom in the long run. These could be genetically passed, although deformities could occurr of course, explaining why Jax has no five fingers, but often came with impressive strenght, a lack of sense for pain as well as rapid regeneration that turned tha lack of pain from a sensorical weakness into an actual strenght.
I kinda want to see Jax meeting Mundo now... he'd be amazed that another Icathian exists - and mourn the state that he is in...