Sorry for coming so late to the discussion.
I’ve really enjoyed it.
We definitely had Liza and Henry and a knife.
I always assumed it was a wooden bucket which had split due to drying out as described by others. Making it entirely unusable as the ‘hole’ goes all the way across the bottom.
But for me the whole point of the song is the psychological ‘game’ being played by Henry who complains about every solution that Liza offers - later referred to as ‘Poor me’ or ‘There’s nothing you can do to help me’ by Eric Berne in Games people play 1964. He doesn’t really want help, he wants attention but passes it off as hopelessness and helplessness.