In the book, there is a lot of death. Therefore, this question is not easy to answer. Moreover, there will be differences of opinion.
First, there is the death of the mice that Lennie holds in his hand. Lennie likes to touch soft things, but he does not know his own strength. So, when he picks up a mouse to touch, he accidentally kills it. If we think that intentionality is important, then Lennie is innocent of anything malicious. Is this responsible? Yes, I would say, but the degree to which he is guilty is small. Accidents happen.
Second, there is the death of Candy's dog. The men complain that it is too old and too smelly. In light of this, the men should put it out of its misery. Carlson suggests it, and the other men agree. Candy capitulates unwillingly. In this case, the men are responsible. But again it is somewhat mitigated, because they had a point.
Third, Lennie accidentally kills Curley's wife. He is responsible, but because it is an accident and Lennie is not all there, his responsibility is mitigated as well.
Finally, George shoots Lennie, as he knows that the men will finally get him and lynch him in a gruesome death. We can say that George's action was an act of mercy killing. In light of this, he is responsible, but he might have made the best decision.
The tragedy of the book is that bad things happen, because the world is so broken. The whole system is broken. The ones, therefore, who are most responsible are the ones who created the system.