“I came from a tough neighborhood,” American stand-up comedian Rodney Dangerfield (1921-2004) used to say. “In the local restaurant, I sat down and had broken leg of lamb.”
 
It’s not known when Dangerfield first used the “broken leg of lamb” joke in his routine, but it has been cited in print since at least 1978.
 
   
Wikipedia: Rodney Dangerfield
Rodney Dangerfield (born Jacob Cohen, November 22, 1921 – October 5, 2004) was an American stand-up comedian, actor, producer and screenwriter known for the catchphrase “I don’t get no respect!” and his monologues on that theme. He is also remembered for his 1980s film roles, especially in Easy Money, Caddyshack, and Back to School.
     
10 July 1978, The Morning News (Wilmington, DE), “Comic gets no respect from sound system” by Otto Dekom, pg. 16, col. 3:
He talked about a restaurant owned by the Mafia in which they served “broken leg of lamb.”
 
27 December 1978, Evansville (IN) Courier, “Scram-Lets” by Clay R. Pollin, pg. 41, col. 4:
About a tough guy: “He owns this restaurant in a very tough part of town. Their specialty is BROKEN leg-of-lamb.”
 
20 July 1980, Marietta (GA) Daily Journal - Cobb County Times, “No Respect: Dangerfield’s Humor Has Roots In Childhood” by Burt Roughton Jr., pg. 3E, col. 3:
“Rough. The clubs I used to play in were rough, I tell you that. One was so rough they served broken leg of lamb.”
 
Google Books
It’s Not Easy Bein’ Me: A Lifetime of No Respect but Plenty of Sex and Drugs
Rodney Dangerfield
Harper Collins, Mar 1, 2005 - Humor - 288 pages
An American comic icon tells the story of his second–act rise from obscurity to multimedia stardom.
 
“When I was a kid,” writes Rodney Dangerfield, “I worked tough places in show business––places like Fonzo’s Knuckle Room. Or Aldo’s, formerly Vito’s, formerly Nunzio’s. That was a tough joint. I looked at the menu. They had broken leg of lamb.”
 
Google Books
That Reminds Me of A Joke:
Outrageous News Stories that Echo our Favorite Jokes
By Editors at Reader’s Digest
White Plains, NY: The Reader’s Digest Association
2015
Pg. ?:
I came from a real tough neighborhood. In the local restaurant I sat down and had broken leg of lamb.
—Rodney Dangerfield
 
Twitter
Rodney Dangerfield‏
@DangerfieldSez
“I came from a tough neighborhood. In the local restaurant I sat down and had broken leg of lamb.” ~Rodney Dangerfield #funny #quotes
10:32 AM - 16 Nov 2016