It occurs to me that it might not be necessary to start with a thesis for or against the death penalty after all. Judgiing from my own thoughts and feelings, it would be hard for me to come out with a thesis statement that the death penalty should be abolished or that it should be retained. I simply don't know. It would be easy to say that the death penalty should be abolished because it is cruel and unusual punishment, because it is unfair to minorities, and because it doesn't deter capital offenses. It would also be easy to say that cold-blooded murderers don't deserve any consideration and that they ought to be eliminated--especially for such atrocities as torture-murders of women and children.
Another approach to a thesis statement therefore might be to state that the death penalty poses a moot question which has yet to be satisfactorily answered. Then the follow-up would be to present the arguments against the death penalty and the arguments in favor. (And there are plenty of people who favor retaining the death penalty and even using it more often.)
This would be a more difficult essay to write, and the conclusion would also be difficult to formulate, but many studies end with the time-honored, all-purpose conclusion that the problem needs further study. After all, your opinion is only one of millions, and your essay is not going to affect the death penalty one way or the other. The same would be true for me if I were to write an essay on the subject. I really don't know. I'm not crazy about the death penalty, but there are many cases I read about in which, to be honest, I certainly can't feel sorry for the person getting the lethal injection.