Dungeon Breaks were a constant risk that all Dungeon cities always had, regardless of whether they had just one dungeon or as many as eight like Lacertilia did.
They usually happened when the glorified monster traps that were dungeons temporarily broke down due to excessive energy concentration, most often caused by overcrowding of monsters within them.
But a dungeon city like Lacertilia which had high levels of adventurer traffic hardly experienced this since adventurers ended up culling the monster numbers frequently.
Even so, the possibility was still there, so the city had measures in place to handle them in the event of them occurring.
First off, there were no organizations or buildings that involved normal civilians within a 5-kilometre radius of each dungeon and the main city.