Whether or not it was justified may be open to debate. What is clear is that we really don't blame George for his drastic action. His motives were pure and understandable--life for Lennie would have been unbearable in whatever circumstances he would have found himself. Lennie would certainly have been frightened and may even have hurt others in his attempt to get to George. We feel George's pain, and we know--bad as it is--it's not the worst thing that could happen to Lennie. It may not be justifiable according to the law; however, we do justify it to ourselves.
George's action of the final scene has long been debated by readers. However, the reader must always evaluate actions of a plot within the verisimilitude created by the author of the narrative, and not on his/her personal opinion. Therefore, within the context of the narrative, George's action is justified, for George knows that Curley and Carlton will injure, if not torture and kill, him before the authorities can take him. In addition, George is aware that even if Lennie can avoid the vindicativeness and cruelty of Curley and Carlton, Lennie will not survive incarceration. For, he is not a rabbit who can be so easily caged.
It is out of his love for Lennie, not malice, that George shoots his friend. Perhaps, Steinbeck prepares the reader for this mercy killing as he so often used animal imagery to describe the mentally-challenged Lennie. (He is bear-like and paws at the water in the first section.) For, animals are often put out of their misery. Even Slim with his "God-like eyes" has told George "you hadda." And, Slim's "word is law." George's actions are consistent with his characterization; so, since Steinbeck does not depart from the verisimilitude of his narrative, George's actions are justified and follow the context of the plot that depicts the desperate and alienated lives of the itinerant worker in the 1930's Great Depression.
Interestingly, there was a film made about the poverty and desperation of people during the Depression who entered dance contests for prizes. In this film, one couple who are so desperately poor enter and struggle to stay on their feet; with their wills ignoring the pain and agony of their bodies, they collapse and die. The title of this movie is They Shoot Horses, Don't They? and the implication, of course, is that these poor dancers should not have been so tortured in their poverty, but, instead, have been put out of their misery--as was Lennie.
I don't think it would have been right for George to let Lennie get arrested. The people who caught him would have hurt him since that's what Curley wanted them to do. That wouldn't have been right since Lennie didn't really do anything morally wrong.
I think it was right for him to kill Lennie because that was his only choice. Lennie couldn't escape and I've already talked about why it would be wrong to let him get caught.