How do I address a female 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".