What does Lennie's attachment to the dead mouse tell us about his character?

Lennie is one of the main characters in John Steinbeck's novel Of Mice and Men. He is mentally challenged, and George has promised his aunt that he will stick by Lennie and take care of him. 
Lennie loves soft things, especially soft creatures like mice and rabbits. However, he does not understand his own strength and often causes harm to animals without intending to do so. The incident with the dead mouse happens very early on in the novel and is part of the exposition. This incident shows us that Lennie is subservient to George like a child is to his or her parent. He did not want George to know what he had in his pocket and tried to hide it from him. Then, when George sees what it is, he quickly denies that he killed the animal. This helps the reader infer that this is not the first time Lennie has killed something without meaning to do so. This also reveals Lennie's need for security and comfort. The mouse is something he rubs, like a worry stone. He likes the way it feels to his hands, which are rough from hard work. Here is the conversation he has with George about the mouse: 

"George looked sharply at him. 'What'd you take outa that pocket?' 'Ain't a thing in my pocket,' Lennie said cleverly. 'I know there ain't. You got it in your hand. What you got in your hand—hidin' it?' 'I ain't got nothin', George. Honest.' 'Come on, give it here.' Lennie held his closed hand away from George's direction. 'It's on'y a mouse, George.' 'A mouse? A live mouse?' 'Uh-uh. Jus' a dead mouse, George. I didn't kill it. Honest! I found it. I found it dead.' 'Give it here!' said George. 'Aw, leave me have it, George.' 'Give it here!' Lennie's closed hand slowly obeyed. George took the mouse and threw it across the pool to the other side, among the brush. "What you want of a dead mouse, anyways?' 'I could pet it with my thumb while we walked along,' said Lennie."