Sounds like Martin Amies's "Time's Arrow", where the man's life is written backwards. That's a book, BTW, not a song.

How about that song -- is it called Dirty Old Man? "I've been around for eighty summers, etc"

"Now I'm Sixty Four", known in Newfoundland and not related to the song by the Beatles. I don't know its history but it has a Victorian feel to it.

I suppose "When This Old Hat Was New". The old man doesn't mention his exact age but mentions things that happened "four score years ago" in the time of Queen Elizabeth I. Since he was a young working man at the time of these events he must have been singing his lament at a great age indeed, and amazingly the same hat seems to have lasted him all those years. Actually this song might qualify for the "dirge" thread.