It was necessary for George to shoot Lennie in the book Of Mice And Men. I can think of many reasons why he had to kill him including Lennie was always getting in trouble and Lennie was mentally ill.
One reason that it was okay for George to shoot Lennie was that Lennie was mentally ill and did not know better. He did not have a high mental capacity, so he did not know when he was doing something wrong until after he had done it and he will continue to do wrong things because he just doesn't know better. I also do not think George wanted to have to take care of Lennie for the rest of his life.
You might want to say that they could have run away and went to a different town, but this is different from all the other times.