Hey Lunies,
I'm sorry to inform you that the "New Lunar Republic" cannot legally exist in its proper location.
The United Nations Treaty on Outer Space states that nobody, nation or individual, may claim land on any celestial body or in space, including on the moon. It says that space and its contents are for everyone's shared use, and anyone from any nation may enter a base of another nation.
So yeah... lol
Don't shoot the messenger