What is Lord Mayor's Court?

Legal Definition
In English law. This is a court of record, of law and equity, and is the chief court of justice within the corporation of London. Theoretically the lord mayor and aldermen are supposed to preside, but the recorder is in fact the acting judge. It has jurisdiction of all personui and mixed actions arising within the city and liberties without regard to the amount in controversy. See 3 Steph. Comm. 449, note I.
-- Black's Law Dictionary
Legal Definition
An English court of limited jurisdiction in both law and equity cases.
-- Ballentine's Law Dictionary