Short answers, pulled from the story.
The title of Lord Mayor is bestowed through letters patent issued by the sovereign. This legal instrument elevates the office from a standard mayoralty to a ceremonial bridge between the city and the crown. The letters patent grant the holder a unique status that is absent in ordinary municipal governance.
Major cities in Australia including Adelaide, Brisbane, Darwin, Hobart, Melbourne, Newcastle, Parramatta, Perth, Sydney, and Wollongong hold the title of Lord Mayor. These cities receive the title as a recognition of their size and importance within the Australian federation. The role is a special status granted by the monarch, distinguishing these capitals from other municipalities.
The Lord Mayor of London holds jurisdiction strictly over the City of London rather than the wider Greater London area. The modern Mayor of London governs the wider Greater London area, while the Lord Mayor of London remains a ceremonial figure. This distinction separates the office from a standard mayoralty and transforms it into a ceremonial bridge between the city and the crown.
Annapolis was the only city in the Thirteen Colonies to receive a royal charter and used the title Lord Mayor prior to the American Revolution. This historical usage demonstrates how the title was once a standard part of colonial administration before being replaced by republican forms of government. The title has evolved from a functional administrative role to a ceremonial one in many places.
The style of address for the office of the Lord Mayors of Belfast, Cardiff, Bristol, the City of London, and York is The Right Honourable. All other Lord Mayors are styled The Right Worshipful, a distinction that refers only to the post rather than the person holding it. The title Sir can be used for salutations when a Lord Mayor is being addressed.