Ok, I’ll attempt to put at least this idea into words.
Battery City is (unofficially) sectioned off into four distinct areas.
1) The Inner City/“City Proper”
2) The Lobby
3) The Outskirts
4) The Underground
The Inner City is what everyone thinks of when someone mentions the city. All pristine and controlled by BLI. The people who live here usually have no idea about what’s really going on outside of the city. It’s basically it’s own bubble and BLI wants to keep it that way.
Everyone thinks that The Lobby is the slum of the city, but that’s not exactly true. It is a slum, yes, but it’s completely artificial. BLI created it as it is and BLI still has complete control over it - only they’re a lot more discrete about it. It’s used as an outlet for BLI’s shadier work and dealings. It’s mostly only inhabited by Droids and the occasional kid from the Inner City who thinks they’re hot shit for running around in there. (Spoiler Alert: they aren’t.)
The Outskirts are the actual slums. It’s where people end up when they’re out of luck or are trying to escape. Whether they’re escaping from the City Proper, or escaping from the desert doesn’t matter. They all end up here. There’s very little access to much of any of the benefits that come with living in the Inner City. (running water, food, education, etc.) There are certain programs in place to keep conditions barley livable, but even then it doesn’t reach everyone. Drac patrols are much more frequent than they are in the Inner City, because it’s the people in the Outskirts that start shit. Besides that, BLI tries to pretend it doesn’t exist. It’s an embarrassment. A blemish on their Better Tomorrow.
The Underground is the realm of the juvie halls. It’s spread out across the city’s various subways systems and tunnels. Much of them existed long before the city did and BLI is unaware of how vast they are. The Underground is split into multiple factions - the two most prominent being the people who activily fight BLI from the inside and the people who trade with the desert. The traders smuggle items in and out - many help distribute food and clothing and such to the people living in the Outskirts. They also smuggle people out of the city and into the desert and vice versa.
Of course, this is just a really broad overview. Within each district, there are subdivisions. (Except for the Lobby, which is too small and controlled to be considered anything other than itself.)