In John Steinbeck's Of Mice And Men, how does Lennie's killing of the puppy parallel his killing of Curley's wife and the mice?

In John Steinbeck's novel Of Mice and Men, Lennie is shown to be very strong and very large, but his intellectual disability makes it difficult for him to understand how strong he is and how much force he puts on the things that he touches. This is evident in the deaths of his puppy, a mouse, and the wife of Curley, the owner of the ranch where they work. All three of them died due to his accidental use of excessive force while "petting" them.

Lennie's friend George, who feels responsible for Lennie and tries to keep him out of trouble, and another ranch hand later discover the body of Curley's wife. Despite George's efforts to explain to the rest of the ranch workers that the death was an accident, most of them still decide to pursue Lennie. When George realizes that there is no way that Lennie can escape the angry, violent mob, he shoots Lennie to keep him from suffering at their hands.