The city was planned to be self-sufficient for 30.000 lower income people. It had a large central square, and a hospital. It was all powered by a Kryptonite-fusion engine deep under the ground.
At the unveiling, Superman overheard Mercy Graves and Luthor talking about a device in place, making him believe there was a bomb under the city. Both Luthor and Captain Marvel tried to dissuade Superman from digging into the ground to the fusion engine, but Superman ignored them. Captain Marvel saw no other option than to use force against him, and it soon escalated into a full blown fight that wrecked the entire city. It was according to Luthor's plan, and even better: he had hoped Superman would destroy the Kryptonite-fusion engine, and the destruction of the city only damaged his image even more. Conversely, Lex Luthor's image was assisted by his gracious acceptance of the situation in front the media outlets who were covering the event including offering to finance the city's reconstruction from his own resources. The media attention caused a greater backlash against the Justice League than Luthor had hoped for.
Lexor City is named after the planet Lexor, first appearing in Superman #164 (October 1963). On the planet, Luthor was considered a hero and Superman a villain.