In the end of the novel, Lennie was unable to change the fact that he had killed a puppy and Curley's wife. In this situation, he really was powerless and was only able to run. Lennie really had no alternative choice or decision to make.
An example where I have felt powerless is actually something that happens more than once in a life time. Seeing a friend upset or hurt puts anyone in such a powerless position, especially if your friend you are trying to help pushes you out. And this really puts you in a powerless position being unable to help someone you care about.