Answer:
The irony in the murder mystery that the police are trying to solve is that they were discussing about the murder weapon which can be under their noses, when in fact, it literally is right under their noses.
Explanation:
The short story "Lamb to the Slaughter" by Roald Dahl tells the story of how a pregnant wife killed her husband with a leg of lamb that she's preparing for dinner. The murder of Patrick, who is a police detective, by his wife Mary and her clever way of disposing her evidence is the climax of the story.
What is ironic about the story is that the police investigating the crime are really and fully unaware of the situation. Just because they are so familiar with the wife, they did not seem to judge her. Also, there is dramatic irony when after being invited or rather requested by Mary to have dinner with her, they agreed and finished the lamb, the very tool used in the crime. And even when they joked that the murder weapon may as well be right under their noses, it literally is right under their noses, on their plates!
The irony in the detectives trying to solve the crime is that they were the ones getting rid of the weapon, literally eating it away.