New Lumos is a man-made island originally built for people to live on, hence the tall buildings. Unfortunately, the distance from the Miitopian mainland, the constant rains, and the permanent state of darkness made the location undesirable by humans. It did, however, become the perfect place for powerful monsters.
When Peculia was first discovered, those who saw the location were unsure whether or not it was just a hallucination, and it was called Hallucinia as a result. For years, humans tried to steer clear of the area, afraid they would go mad, until scientists later confirmed that this place was in fact real, and it was renamed Peculia due to its peculiar nature.
The Tower of Despair is all that remains of the time before Miitopia. The monsters found there were originally fully block-patterned, but, after centuries, they eventually started to lose some of their panels, leaving behind blackness.
The Sterile Plant originally had workers. When they heard of the Dark Lord's attacks, however, the workers fled and haven't returned since.
The Sinister Plant was originally a functioning factory but was abandoned after exactly 7 robot uprisings. Corrupt scientists then took over and converted it for their purposes.