On the great supporting structures huge lights, now unlit, would come on when the Moon passed behind the Earth, depriving the city of sunlight.
As long as astronomical questions are fair game, what you're describing is a lunar eclipse, which happens every few years.
However, the city would be deprived of sunlight for two weeks of every month just by the rotation of the moon. The moon does not rotate with respect to the Earth, but it does with respect to the Sun. That's why we have new moon, quarter moon, full moon, etc. It's not the Earth getting in the way, it's the body of the moon itself.
As you point out, though, the Earth is always in the sky and would be bright when the Sun is not in the sky.
I don't usually enjoy stories without Lois (even though Lori is kinda-Lois), but your stories are always great, and this one looks to be no exception!
