Why is the conversation between Mary and the grocer important?
Mary has a conversation with the grocer for several reasons. For one thing, she wants to use him as an alibi. She wants the police to believe that her husband Patrick's murder occurred during the time she was out of the house buying groceries. She wants to allow the fictitious murderer as much time as possible to sneak into the house, kill her husband, and then slip away. She also wants to give that frozen leg of lamb some extra time to cook in the oven before she goes back home, "discovers" Patrick's body, and phones the police. Going to the grocer and spending as much time there as is reasonably possible will give her an extra fifteen or twenty minutes before she has to make that phone call. She doesn't know how long it will take to cook a leg of lamb that is frozen solid, so she wants as much time as she can get. An example of how Mary extends the visit to Sam the grocer is seen in the following dialogue:
"Anything else?" The grocer cocked his head on one side, looking at her pleasantly. "How about afterwards? What you going to give him for afterwards?"
"Well-what would you suggest, Sam?"
The man glanced around his shop. "How about a nice big slice of cheesecake? I know he likes that."
"Perfect," she said. "He loves it."
"Lamb to the Slaughter" was first published in Harper's Magazine in 1953. Those were the days in which there were still many small grocers and the proprietors knew their customers personally and had time to chat with them. Nowadays, as we know, the supermarkets dominate the grocery business and at best a customer has a few seconds to talk to the checkout clerk before being pushed out by the next customer in line. (John Updike's short story "A & P," published in 1986, gives a more up-to-date picture of what a typical supermarket is like.)
Sam is just about the only possible alibi for Mary because she leads such a confined domestic life that she rarely sees anybody but the grocer and her husband. Going shopping must have been a big adventure for her. It will not seem like too much of a coincidence that Mary was at the grocery store when the murderer killed her husband. The perpetrator might have been lurking outside and peeking through windows, then seized the opportunity to do the deed when he saw her leaving to go shopping.