I think a Nuzlocke or similar challenge roleplay would need to build a universe centered around the rules rather than have Nuzlocke-esque elements be used as an added-on mechanic to an ordinary adventure.
Nuzlocke in essence only has two rules: Pokemon who faint are dead, and catch the first encounter on a new route. Decide on an interesting 'Locke variant and craft a universe around it to justify or support it. But it clearly would take on a mature route, that Pokemon are feral creatures intent on killing to assert their dominance.
Which gives me another idea: What if we were hired by a rogue, non-profit coalition of "professors" to capture animals infected with the virus known as Pokerus, which, untreated, mutates animals into what we know as Pokemon. We're trying to capture different strains of the case to return back to base of study for a cure, but the government would prefer new cases be round up and trained for use as bioweapons of war, as a kind of arms race against another afflicted region whose government is harnessing the fact that Pokemon exhibit not only unique scientifically-explained abilities, but a violent nature against others that have become mutated--so the more they are trained, the more disparity in their advantages should a rival government try to challenge fire with fire late in the game. Government workers for the round up operation are called Trainers, and workers of professors are Aides. Due to Pokemon's violent nature towards each other, Trainers and Aides often get into battles as their interests out in the field clash.
Or something. It's a really rough idea I just came up with on the phone and personally don't care for, but some might like it.