Was George correct in his decision of killing Lennie?
Well, I don't know that there is a right or wrong answer to this question, so it is one that each person would have to decide for him or herself. It hinges a lot on the meaning of the word "correct." I am going to assume that what you mean by this is "Did George make the correct choice in killing Lennie?"
Still, how do we define "correct?" It's not the same thing as "right vs. wrong" in a moral sense. What you're asking, essentially, is "would most people in a similar situation act in a similar way." That is a fair assumption of "correctness." Again, though, notice that this is different than asking if it was morally right or wrong to do.
So the question remains...did George make the right call?
The answer: Maybe.
Who can really say? George made the call that he felt he had to make. God knows what would have happened to Lennie had they caught up with him. Knowing the time period, the most likely result is that they would have strung him up from a tree, a tortuous way to die. At best they would have probably beaten and arrested him, after which he would have either been put in jail for the rest of his life (which would probably mean a brutal work camp) or housed in an asylum (which, at the time, might have been worse than death!)
At either rate, George made the decision to kill his best friend to help him avoid that kind of suffering, suffering he wouldn't have truly been able to understand. In George's mind, of course, it was a mercy killing. Based on the evidence, it is hard to argue with his logic.
There you have it: in my humble opinion, I would have to say that George made the correct decision in helping his friend avoid a fate worse than death (though, as I said, it is likely he would have been killed by the "mob" in a far more brutal way.) In this case, George must be given the benefit of the doubt. He felt he was responsible for Lennie, and loved him. In that capacity, he couldn't let Lennie die like a dog at the hands of the angry posse.
In my opinion, I think he had to do it. George knew Lannie was going to suffer if he didnt kill him. Curley was going to make him suffer and have revenge for previously crushing his hand. Curley promised to shoot Lennie in the guts and that would be very painful. Even if Curley wasn't gonna kill him, he would've jailed him and abuse him. Instead of that, George took lennie to the river and told him about their dream so he was happy, then shot him in the back of the head. He saved lennie a terrible horrifying death. I think it was the right choice.