In Chapter one, the audience learns that Lennie acts like a child and George seems to be his guardian. In this scene, George finds out Lennie has been petting a dead mouse on their journey. When George throws the mouse into the river, Lennie goes back to get it and when George asks for it back, Lennie begins to cry. Lennie is like a toddler that seeks comfort from a soft object like a blanket, a teddy bear, or in this case a dead mouse.
In chapter two, Candy becomes familiar with George and Lennie. Candy begins to gain their trust and they become friends. This lets George and Lennie know that they aren't the only outcasts. Candy tells them and warns them about Curley and his wife.
In chapter three, Lennie shows his aggressive and potentially deadly side. Curley starts fighting Lennie and Lennie wasn't defending himself until George urged him to. Lennie ends up brutally crushing Curley's fist. After Lennie snaps out of his violent phase, hr breaks down in George's arms saying he didn't want to hurt him. Lennie doesn't know how strong he truly is so when he gets violent, it becomes devastating for everybody.
In chapter four, Crooks taunts Lennie about George's whereabouts. Implying that George is somewhere hurt or dead and he's never coming back for Lennie. Crooks goes on to tell him that Lennie would be taken away and put in an asylum where he'd be chained up like a dog. Lennie began to grow angrier and angrier. Lennie is as protective over George as George is of him.
In chapter five, Lennie ends up in the barn alone with Curley's wife after he kills a pup. Lennie keeps telling her that he shouldn't be talking to her but she just ignores it. He tells her about how he likes to pet soft looking things and then she invites him to pet her hair but he started to mess it up and she was resisting and yelling. That only caused Lennie to panic and he shook her so violently, he snapped her neck and killed her. This time Lennie's strength has killed something much bigger than a mouse or a puppy.
In chapter six, Lennie is on the run but he remembered to go back and hide in the brush if anything ever went wrong so George could find him. George finds Lennie and they talk about their dream of owning their own ranch. George knows that he has to kill Lennie before the rest of the guys find them so George talks about their dream together to soften the blow. Then he takes the shot right to the back of the head. This connects to Candy's relationship with his dog. George most likely learned that him killing Lennie rather than a stranger would be the most merciful to the both of them.