They built the city underground, beneath Robotropolis, where it remained hidden for all eleven years. When Griff brings Sonic, Sally, and Antoine to Lower Mobius, Sonic comments that they've heard of Mobians who built an underground city, but Robotnik seems unaware of its existence.
A large energy crystal in the roof of the cave is both a power source and light source for the city. The entrance(s) are hidden and can only be reached by underground tunnels and pipelines, which are patrolled by Ratbots built and abandoned by Robotnik. They keep unwanted intruders out of the city, but also pose a danger to the people in Lower Mobius. To keep the Ratbots out of the city, large metal doors block off the pipelines that lead to it.
All of the citizens of Lower Mobius appear to be either goat, pig, wolf or monkey species. They have attempted to continue on with a life as close to life in Mobotropolis was by having parks, growing flowers, opening shops and restaurants, etc. but none of the residents seem interested in fighting back.