Green’s Dictionary of Slang

(US black) a very large or infinite number.

1893		H.A. Shands Speech in Mississippi n.p.: Lebenty-lebem [...] Negro pronunciation for eleventy-eleven, an expression for an indefinitely great number [DARE].
1917		S. Lewis Job 35: ‘They’ll keep their gum and a looking-glass in the upper right-hand drawer of their typewriter desks, and the old man will call them down eleventy times a day’.
1925		Labor Age 14-15 12/2: They’re trying to make out that the young girl who married a millionaire is a Black Beauty, even though her family lived eleventy- eleven years in Wales.
1942		Berrey & Van den Bark Amer. Thes. Sl.
1985		in DARE.
1993		J.D. Barrett Quiet Crazy 22: Just like eleventy-eleven other times with Mama.
1994		T. Wolff In Pharoah’s Army 91: [T]he Chinook was a couple of feet over my head, just hanging there, all lebenty zillion tons of it.
2003		M.D. Hunt Perfect Turkeys 143: I’m sure she’s counted all eleventy-eleven of them.