In "Lamb to the Slaughter," how does Mary's pregnancy influence the story?

Mary's pregnancy makes it all the more shocking that her husband is planning to leave her. She is six months pregnant—very far along for him to decide to bail out of the marriage. Further, the coldness with which her husband delivers the news must also be shocking. He says to her:

But there needn’t really be any fuss. I hope not anyway. It wouldn’t be very good for my job.

We can imagine her rage growing as he exhibits more concern for his job than for their unborn child. This blow also comes completely out of the blue. She loved her husband up until this point, looking forward to his coming home from work as her "blissful" time. She liked being with him and even enjoyed the way he sat in his chair.

When she finds out he is divorcing her, her initial response is disbelief and denial. She then kills him quickly with the frozen lamb, not even thinking about what she is doing until after he is dead.

Her knowledge of having a child to protect and her desire that it not be orphaned then influences Mary to cover up her crime.

The fact that Mary is pregnant has two influences on the story.  One is directed at the reader and the other is a direct influence of Mary's actions.  

Mary's pregnancy influences the reader by making the reader sympathetic to her and her actions.  She is a soon to be mother, which is going to be a ton of work.  According to my wife, being pregnant is no walk in the park either.  So the fact that she is pregnant immediately causes the reader to want to protect her.  Those protective feelings continue to grow after Patrick announces that he is leaving her.  We care for Mary, not Patrick.  

Mary's pregnancy also influences her actions.  I think that Mary would have confessed to her actions and taken whatever punishment was given to her, if she was not pregnant.  The text indicates that she knows what her punishment will likely be, and that it would be a relief.  She doesn't know what will happen to her unborn child though, and that fear motivates her to find a way to get away with her crime.  She's not willing to risk the baby's life for her crime.  

As the wife of a detective, she knew what the punishment would be. It made no difference to her. In fact, it would be a relief. On the other hand, what about the baby? What were the laws about murderers with unborn children? Did they kill them both -- mother and child? Did they wait until the baby was born? What did they do? Mary Maloney didn't know and she wasn't prepared to take a chance.

Does Mary's pregnancy influence the story in "Lamb to the Slaughter"?

Mary's pregnancy has an effect on the story in a number of ways. It naturally makes her a more sympathetic character, so the reader can continue to identify with her even after she commits a brutal murder. The fact that she is expecting the baby in a few more months makes her completely dependent on her husband Patrick emotionally, financially, and in every other way. Thus her reaction to his totally unexpected announcement that he is leaving her comes as a terrible shock and makes it more plausible that she should succumb to a sudden impulse to kill him with the frozen leg of lamb she just happens to be holding. Furthermore, her instinct to get away with her crime is more understandable in view of the fact that she wants to keep her baby. If she went to prison, the baby would be taken away from her and she would never see it again. Mary remains a sympathetic figure because she is thinking about her unborn child rather than about herself. After the murder:

It was extraordinary, now, how clear her mind became all of a sudden. She began thinking very fast. As the wife of a detective, she knew quite well what the penalty would be. That was fine. It made no difference to her. In fact, it would be a relief. On the other hand, what about the child? What were the laws about murderers with unborn children? Did they kill them both-mother and child? Or did they wait until the tenth month? What did they do?

The fact that Patrick decides to walk out on his wife when she is six-months pregnant reflects unfavorably on him. It makes Mary's enraged reaction more plausible and induces the reader to overlook the fact that Mary is technically guilty of something like aggravated manslaughter. Most readers want to see Mary get away with her crime because she is the innocent victim of gross injustice.

Would Mary have killed Patrick if she had not been pregnant? Probably not. She would have lacked the last elements of outrage that gave her the strength and motivation to wield the weapon.

At that point, Mary Maloney simply walked up behind him and without any pause she swung the big frozen leg of lamb high in the air and brought it down as hard as she could on the back of his head.

Is Mary pregnant in "Lamb to the Slaughter"?

Mary Maloney is a doting wife, and as the story opens, she eagerly anticipates her husband's arrival home from work. As she sits tranquilly, she watches the clock with the pleasant expectation that every minute which passes brings Patrick closer to her. It is at this point that we learn that Mary Maloney is also expecting their first child:

Her skin—for this was her sixth month with child—had acquired a wonderful translucent quality.

Although we don't typically use the phrase "with child," this was common phrasing at the time the story was written, in the early 1950s. At that time, discussing pregnancy was considered a delicate subject, so people often circumvented direct phrasing and tried to express the condition with a softer connotation.

Mary is six months pregnant, and it is noted that her skin has the glow of happily pregnant woman. Ultimately, this makes Patrick's news all the more despicable. He's not only leaving a wife who adores him, but delivering this bombshell to a wife who stands before him visibly carrying their first child. Patrick has presumably been having an affair (the story leaves out the details of that conversation), and he plans to leave his child as well.

This also factors into Mary's decision to cover up her crime. She is desperate to save her unborn child because she isn't quite sure what happens to pregnant women accused of murder:

It made no difference to her. In fact, it would be a relief. On the other hand, what about the child? What were the laws about murderers with unborn children? Did they kill them both—mother and child? Or did they wait until the tenth month? What did they do?

Mary Maloney isn't willing to risk it. She will not allow the fate of her unborn child to be compromised because of her reaction to Patrick's news, so she quickly develops the perfect alibi for her crime.