From Gineipaedia, the Legend of Galactic Heroes wiki
Luna City, sometime referred to simply as 'the lunar city,' was a large city built on the Earth's moon in the mid-22nd century by the United Earth Government. Luna City served as the headquarters of the Ministry of Space (and, therefore, likely served as the headquarters for the UEG's Space Force as well) and by 2166 Luna City had a greater population than the UEG capital of Brisbane, Australia.(LOGH: 'To Earth')
- Luna City is not mentioned in any contemporary context in the logh OVAs. This may indicate that the city was destroyed, or rendered uninhabitable during the Earth–Sirius War.