To say that George killed Lennie out of friendship would be overly sentimental. Steinbeck was writing a realistic or naturalistic novel and trying to show how such things as George's killing Lennie can and do happen in real life. Lennie has good and bad qualities. George has good and bad qualities. None of these men are noble, and Steinbeck doesn't want to pretend they are. George kills Lennie for a whole variety of reasons, one of which is to save him from being tortured and killed by the pursuing lynch mob. But George is obviously interested in saving himself, both from the lynch mob, who might decide that he was implicated in the death of Curley's wife, as well as from the law, who might arrest him for murdering Lennie. George is also concerned about eliminating a man who is becoming a menace to society, a man who might even be described as a monster.
When the men are organizing to pursue Lennie at the ranch, Curley calls to George:
"You George! You stick with us so we don't think you had...
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