That would depend if the frozen lake was natural or artificial.
It's hard imagining life for the average person in the Silver Millenium when there's barely any flashbacks to show off.
I actually use another anime as my point of reference like Log Horizon or Yugioh Arc-V but I can understand why fans think the Silver Millenium's technology is equivalent to 16th century France and its economy is still feudalistic.
Wasn't the PGSM version of the moon kingdom had a dome like Atlantis?