Green’s Dictionary of Slang

(US) to eat.

1944		Cab Calloway New Hepsters Dict. in Calloway (1976) 256: grease (v.): to eat.
1946		Mezzrow & Wolfe Really the Blues 219: I ain’t greased since the big bean collared a nod in the early black.
1954		‘“Hipster” Rev. Dict.’ Mad mag. Oct. 20: eat – grease.
1959		Jazz for Moderns 20: grease: food, or ‘to eat’.
1967		Current Sl. I:4 1/2: Grease, v. To eat.
1977		E. Bunker Animal Factory 126: I go grease in the kitchen every night.
1982		W.D. Myers Won’t Know Till I Get There 22: Earl [...] he was greasing away on a chicken thigh.
1996		Eble Sl. and Sociability 31: Sometimes the word + particle construction is typical of and strengthens the synonymy of a group of related verbs: blimp out, chow down, grease down, hone out [...] all mean ‘to eat, usually quickly or in great quantity’.
2000		F.X. Toole Rope Burns 44: After the weigh-in tomorrow, I’m goin down to the buffet and greeze.
2018		I. Welsh Dead Man’s Trousers 78: Once we’d onlysit down to grease in some grubby Leith cafe together.