Short answers, pulled from the story.
Lord mayor is a title granted to the head of certain major cities across the Commonwealth and the former British Empire, with special recognition from the sovereign of the United Kingdom. Aldermen usually elect the lord mayor from among their own ranks.
Australian cities with lord mayors include Adelaide, Brisbane, Darwin, Hobart, Melbourne, Newcastle, Parramatta, Perth, Sydney, and Wollongong. The monarch grants this special status to the mayors of these major cities.
Niagara-on-the-Lake is the only town in Canada with a lord mayor in the traditional sense. The title recognizes its history as the first capital of Upper Canada.
Walter Gretzky was appointed honorary Lord Mayor of Brantford by the town council, alongside its regularly elected mayor. This is the only known case of a council granting the title itself, rather than the Crown or a national government.
The Lord or Lady Mayor of London holds jurisdiction only over the City of London. The modern Mayor of London, by contrast, governs the whole of Greater London.
Lord mayors of Belfast, Cardiff, Bristol, the City of London, and York are addressed as The Right Honourable. All other lord mayors are addressed as The Right Worshipful, and Sir can also be used in direct address.