George kills Lennie out of love. He has been taking care of Lennie and knows his limitations. If you consider the alternative to George killing Lennie, you understand why George kills him. Lennie would be hunted down by men with guns. He would be taken and put in jail, put on trial, and then sent to prison. George knows what this would do to Lennie. He realizes it is kinder to kill him than put him through an ordeal that Lennie would never understand or be able to cope with. In this case, killing Lennie is the most humane thing George can do for his friend.
Given the time that the novel occurs, George had not other choice. First, if Lennie would have been brought to trial, he would not have understood what was going on. His mental capacity would not have allowed him to assist in his defense. It would have been a railroad job sending him down the river (similar to the situation in TO KILL A MOCKINGBIRD). Second, if there was a way to have the courts declare Lennie mentally "insane" or incapable of understanding the "wrongness" of his actions, George knew that he would have been placed into an instution for the crimminally insane. Here he would have been mistreated and probably physically and sexually abused. Third, there is the strong possibility that their could have been a mob lynching mentality takeover by the others on the ranch. In all three cases, George knew that Lennie would and could not understand what was happening -- solution, let his spirit free.
Well i think if you asked Steinbeck, he would probably say that it was the only solution. And i think i would have to agree with him. If George had not killed Lennie, and rather, had ran away with him, the same thing would have happened over again. As witnessed by the puppy and bunny that Lenny crushed, Lenny simply didn't know his own strength. Since neither George nor Lennie had any money, they would have had to stop and work, and be around people, and Lennie would have gotten in trouble again. Obviously given Lennie's temperment, George couldn't leave him. The only other solution, then, was to have the other men find Lennie and shoot him themselves. However, in that scenario Lennie would have been frightened and confused. This way he died thinking about the thing he wanted most in the world: his own farm with george.