Green’s Dictionary of Slang

(US) a fast-food café.

1907		Indianapolis Star (IN) 25 Sept. 3/4: Up on the seventh floor of the Board of Trade building [...] and just seven floors above the ‘one-arm lunch’.
1912		M. Nicholson A Hoosier Chronicle 297: Everybody’s saying ‘Stop, Look, Listen!’ [...] the white aprons in the one-arm lunch rooms say it now when you kick on the size of the buns .
1915		Wash. Post (DC) 28 Feb. 4/1: The remaining characters are [...] a one-armed ‘joint’ proprietor, and the humbler chronicler hereof.
1915		Morn. Tulsa Dly World (OK) 13 June 19/3: One-arm joint — A chair dairy lunch.
1917		O.O. McIntyre New York Day by Day 9 Mar. [synd. col.] A bell-boy from the Ritz eating in a one-armed lunch.
1922		M.E. Smith Adventures of a Boomer Op. 28: I was setting in one of these one-armed man’s restaurants, eating ‘hot dog’ and trying to figure out some way to stop the war.
1928		J. Callahan Man’s Grim Justice 189: I ate in [...] one-arm lunch rooms.
1928		Hecht & MacArthur Front Page Act I: When you’re crawling up fire escapes [...] eating Christmas dinner in a one-armed joint, don’t forget your old pal.
1931		D. Runyon ‘Breach of Promise’ in Runyon on Broadway (1954) 17: The Tuesday string of one-arm joints where many citizens go for food and wait on themselves.
1940		J.H. O’Hara Pal Joey 29: She went with me to this one-arm where I eat.
1949		N. Algren Man with the Golden Arm 291: The one-arm restaurant [...] that carries junkie traffic all night.
1958		Murtagh & Harris Cast the First Stone 13: They [i.e. prostitutes] hang around the one-arm joints where people eat standing up.
1991		(con. 1920s) O.D. Brooks Legs 110: Then I’d buy a paper and go to Thomson’s, a one-armed cafeteria, where I’d read the news over coffee.