Atticus and George each tried to take responsibility for a man who was powerless on his own. Tom Robinson had no way of protecting himself against the bigotry of white society that existed in 1930's. Lennie Small had no one to protect him against the bigotry and hatred that existed in the 1930's towards the mentally challenged. So both men tried, but ultimately failed, to be responsible for these men but they were both defeated by societal forces beyond their control.
You might begin by thinking about the word "responsibility." How do you define a responsible person? Someone who tells the truth? Keeps his word? Does the right thing? Meets his obligations? Get a clear idea of how you define responsibility.
Next, make 2 lists, one for each character. Write down every important thing the character did or said. Then, based on each list, would you say that each character is responsible or not? Compare the two lists. Is one character more responsible than the other? Are both characters very responsible? Are they irresponsible? Your answers will direct you to a thesis statement. Your thesis is a statement about the characters that you can explain and support with evidence from the literature.
Another way into your thesis might be this idea. Assume that both men are responsible men. Now ask questions. Did they pay a price for being responsible? Were they rewarded for it? Did others benefit because they were responsible? Your answer to each question could be a thesis for a paper.
Remember to do some prewriting and to think about what comes to mind. Good luck!