A Lord Mayor is the chief citizen of a UK city and it is an honour bestowed on the city by the Sovereign.
In the Scottish cities of Aberdeen, Dundee, Edinburgh and Glasgow the equivalent position is Lord Provost.
Not all cities have a Lord Mayor. See Cities that Elect a Lord Mayor
The Lord Mayors of London and York and Belfast (and the Lord Provost of Edinburgh) have been styled 'The Rt Hon' since time immemorial. This privilege has also been granted by the Sovereign to the Lord Mayor of the city of Cardiff (and the Lord Provost of Glasgow).*
The remainder are styled 'The Rt Worshipful' (unless they are a Privy Counsellor in which case the style used is The Right Honourable The Lord Mayor of X). The Lord Mayor of Westminster is referred to as 'The Rt Worshipful The Lord Mayor of Westminster'.
* Note these Lord Mayors and Lord Provosts are styled 'The Rt Hon', but the style refers to the office rather than the person (unless of course the Lord Mayor also happens to be a Privy Counsellor). Thus 'The Rt Hon the Lord Mayor of York' is correct, but 'The Rt Hon John Smith' is not.
How to Address a Lord Mayor
There is no difference in the form of address for a Lord Mayor who is female.
The recommended social form of address is as follows:
|Beginning of letter||Dear Lord Mayor|
|End of letter||Yours sincerely|
|Envelope||The Rt Hon the Lord Mayor of X, or The Rt Worshipful the Lord Mayor of X or The Rt Worshipful the Lord Mayor of Westminster|
|Verbal communication||My Lord Mayor or Lord Mayor|
|Description in conversation||The Lord Mayor or The Lord Mayor of X|
|Social joint invitation**||The Lord Mayor and Lady Mayoress of X|
If desired, the name (preceded by Councillor) may follow the office (not applicable to the Lord Mayor of London), but 'The Rt Hon' or 'The Rt Worshipful' should always be placed before 'the Lord Mayor'.
**Note that, traditionally, invitations, when sent to the home address, are addressed to the Lady Mayoress alone, with both names being inscribed on the invitation card. It has become increasingly acceptable, however, to address the envelope with both names.
The Lord Mayor takes precedence when he is hosting civic events.
For precedence and protocol at events that are staged in the City of Westminster contact the Private Secretary to the Lord Mayor of Westminster who liaises between the offices of the Lord Mayor, the Lord-Lieutenant and the Mayor of London.