"Lamb to the Slaughter" is essentially a perfect-crime murder story told with a touch of humor. There are two major kinds of perfect-crime murder stories: those in which the the murderer thinks he has planned the perfect crime but gets caught because of something he overlooked, and those in which the murderer actually gets away with it. Edgar Allan Poe may have invented both of these genres. Examples of the former are "The Tell-Tale Heart" and "The Black Cat." Poe's story "The Cask of Amontillado" is an example of a crime in which the perpetrator gets away with it completely.
Mary Maloney commits the perfect crime, but she doesn't plan it ahead of time. She acts spontaneously, using the weapon which happens to be in her hand, a frozen leg of lamb. It is significant that she is a cop's wife, because she has learned a lot about police work from listening to her husband and his friends. She sets up an alibi by going to the grocers and letting it appear that her husband was killed by an intruder in her absence. Before leaving the house she turns the oven up as high as it will go and puts the frozen leg of lamb inside.The reader might wonder how long it will take to cook the lamb, so Dahl answers this question by having Mary discuss it with Sam the grocer.
"No, I've got meat, thanks. I got a nice leg of lamb, from the freezer. . . . I don't much like cooking it frozen, Sam, but I'm taking a chance on it this time. You think it'll be all right?"
"Personally," the grocer said, "I don't believe it makes any difference."
The prolonged conversation with the grocer strengthens Mary's alibi by extending her absence from home.
The facts that there are so many policemen assigned to the investigation and that they stay so late searching the premises for the murder weapon, provides Mary with an excuse to invite them to have dinner. If they weren't well acquainted with Mary and her husband, they wouldn't violate protocol by accepting her invitation; but since her husband was "one of us," they regard Mary as "one of us" as well. This is a ticklish plot problem--how to get the cops to eat the evidence.
There was a great deal of hesitating among the four policemen, but they were clearly hungry, and in the end they were persuaded to go into the kitchen and help themselves.
Because her husband was a cop, the other detectives and uniformed officers spend an unusually long time on the investigation, thus giving the lamb enough time to thaw and cook. Time was another plot problem for Dahl to solve. All he had was the idea of a wife killing her husband with a frozen leg of lamb--but then he had to give her enough time to cook it in order to commit the perfect crime by disposing of the murder weapon. A big piece of meat frozen solid obviously takes a long time to cook. Normally, she probably would have let it thaw out overnight and cooked it the next day, but under the circumstances she had to speed up the whole process and have the lamb ready for the hungry men within about four hours. Patrick came home right at five o'clock, and it was a little after nine when she felt safe about serving dinner.
The search went on. . . . It began to get late, nearly nine she noticed by the clock on the mantle.
eNotes Study Guide for "Lamb to the Slaughter" discusses five other themes. These are Betrayal, Identity, Love and Passion, Passivity, and Justice and Injustice. See reference link below.