Not to scare elmore again, but -

Someone on the All That Chat board suggested that Angela Lansbury's next role should be as one of the Brewster sisters in Arsenic and Old Lace. Someone else mentioned that her memory isn't what it used to be, I thought Trevor Nunn, Memory - so i have to investigate:
Can a somewhat serious lyric be considered a parody, or does a parody have to be funny?
If Trevor Nunn directs her in ARSENIC AND OLD LACE:(tune of "Memory")
Eighty
And still here in my make-up
I can dream of the next role
And I wish you the same
Past the footlights
The happy crowd jumps up on their feet
The same people
Cheered my Mame
Mem'ry
Every morning I wake up
And remember the old days
I was glamorous then
In their cheering
They say that I'm still glamorous now
Does that mem'ry
Live again
Burnt out friends, some classic plays
The smell of elderberry
I'm no booster
Of the sisters Brewster
But working keeps me merry
Laughing
I can still get them laughing
Then they stop for a moment
As they wipe off a tear
While they're laughing
I hope this play's a limited run
So the next job can be here