The current Lord Mayor of Brisbane (2009) is Campbell Newman.
currently the mayor of the city of adelaide is Stephen Yarwood
Lord Mayor is the title of the Mayor of a major city. Great Britain is a country and as such doesn't have a Lord Mayor.
In writing, as 'Lord Mayor', perhaps surprisingly. The title Lady Mayoress is reserved only for the wife of a Lord Mayor. You should address a female Lord Mayor as "Madam Mayor" in conversation. It is considered impolite, certainly in public speaking, to address her just as 'mrs. Smith'.In writing an envelope, you use "Mrs. J.B. Smith, Lord Mayor of Portsmouth".
"The Right Honourable Lord Mayor"
Yes, "Lord Mayor" should be capitalized because it is a title referring to the mayor of a city or town.
Thomas Hayes - Lord Mayor - died in 1617.
John Frederick - Lord Mayor - was born in 1601.
John Frederick - Lord Mayor - died in 1685.
Isaac Penington - Lord Mayor - was born in 1584.
Isaac Penington - Lord Mayor - died in 1661.
Edmund Wright - Lord Mayor - died in 1643.
Edward Barkham - Lord Mayor - died in 1634.