Was George justified murdering Lennie ?

George was justified killing Lennie because he doesn't have to babysit a grown man who has the mind of an child . Even if George is not justified he should be because Lennie has been nothing but trouble,first he was tugging a young lady's shirt when she had gotten frightened and had said to "stop" so they had run away ,second he got into a fight with candy and broke his hand ,third he killed the pup that slim had gave him and lastly he murdered a girl by stroking her hair when he sexually harassed her. If George wouldnt have shot lennie then Ill rather just shoot myself .