Katy Bar the Door

I do not know if this is the origin but for Katy Bar the Door:

Katy bar the door
Lock and latch it
Here comes Lizzie
With a brand new
Hatchet

with reference to Lizzie Borden

Lizzie Borden
took an axe
and gave her father
forty whacks

and when she saw
what she had done
she gave her mother
forty-one

The verse to the song "Lizzie Borden," sung by the Chad Mitchell Trio in 1961, is actually,

"Shut the door,"
Lock and latch it.
Here comes Lizzie with a brand new hatchet.

Katie bar the door has nothing to do with this song.