Neu Hiraleon was the government centre in Hekseville in Gravity Rush, before being taken away by a gravity storm in Gravity Rush: The Animation - Overture, and then reappearing as the Lost City in Gravity Rush 2. It features a gravity engine which allows it to float in the air (similar to the islands of Jirga Para Lhao), and it can eventually use its external body to cause physical devastation after being taken over by Nevi. After travelling through the gravity storm, it ended up in the Candle Zone.

During Gravity Rush, Adreaux gathered data in Hekseville to bring back to Neu Hiraleon, where Project Sea Anemone was being developed. Eventually when its development was complete, Adreaux, with Mayor D'nelica's permission, released it in Vendecentre.

Throughout Gravity Rush: The Animation - Overture, Kali and Durga were kidnapped by Dr. Brahman, who placed them in cradles for experimentation at Neu Hiraleon.

During the second episode of Gravity Rush: The Animation - Overture, an announcement was made in Hekseville warning citizens of Neu Hiraleon's strange gravitational activity. Kat and Raven went to go investigate the government center where they found some strange cradles containing orphaned children, but confronted by an odd security robot. After Raven gives it a swift kick, the girls are then encountered by a pair of cyborgs. These cyborgs, ordered by Dr. Brahman, had tampered with the gravity engine which in turn resulted in it malfunctioning and then creating the level 4 alert. Syd arrived and assisted Kat and Raven as they fought the cyborgs, but they soon ended up self-destructing, leaving Kat, Raven, and Syd with the escalated level 5 alert. They were unable to escape it, as they, along with Kali and Durga, ended up being pulled in by the horrific storm.

At some point during Gravity Rush 2, the Council came upon a rift leading to a mining site where the Lost City was located, though they did not know it was the Lost City at the time. They sent a patrol to investigate the free-oscillating gravitational waves that was present at the mining site. The patrol made it to the Lost City, and they made documentation there; however, they were ambushed by Nevi to which resulted in them losing communication with the Council.

Kat and company don't actually visit Neu Hiraleon itself until the second episode of Gravity Rush: The Animation - Overture, despite the location making an appearance in Gravity Rush.
Since the government centre disappeared with Neu Hiraleon, the police HQ was relocated to the clock tower in Vendecentre. The government centre has no single location, however.
It is unclear why exactly the gravity engine take the shape of a human skull, but it is not the first thing seen in the environment resembles a human body part (i.e. the teeth shaped platforms surrounding the World Pillar, and the spinal cord like structures of its interior in the lower areas).