I checked the sheet music (See Masato's link). Only a few words are different from the ones posted by Ralph Butts above, but they are significant. I have put them in boldface:

I'M TYING THE LEAVES SO THEY WON'T COME DOWN
Words, E. S. S. Huntington. Music, J. Fred Helf.
New York: Helf & Hager, 1907.

1. Playmates were they, girl and lad.
She's home today. lad feels sad.
Doctor who calls, whispers low,
"When the last autumn leaves fall, then she must go."
Lad with a tear climbs a tree.
"I'll keep her here," murmurs he.
Big man in blue sternly cries,
"What are you doing there?" Lad replies:

CHORUS: "I'm tying the leaves so they won't come down, so the wind won't blow them away,
For the best little girl in the wide, wide world is lying so ill today.
Her young life must go when the last leaves fall. I'm fixing them fast so they'll stay.
I'm tying the leaves so they won't come down, so Nellie won't go away."

2. Sad mother grieves, day by day,
Watching the leaves, hears boy say:
"You mustn't cry, for, you see,
I have tied all the leaves fast up on the tree."
Doctor brings joy one glad day.
Mother tells boy, "Nell will stay."
Lad at girl's side, cries with glee:
"That's what I said one day in the tree. CHORUS