Green’s Dictionary of Slang

(US) for an owner of a nightclub or restaurant to pay a customer’s bill.

1946

E. Wilson Pikes Peek or Bust 231: Toots’s [i.e Shor]customers often note that he ‘seldom puts the Otis on the grunt’ Philologists may be interested in that expression. The grunt is the check; ‘giving the Otis’ refers to ‘lifting,’ from Otis elevator.