What was author Harper Lee trying to teach readers about morals and ethics in To Kill a Mockingbird?

One thing Harper Lee teaches in To Kill a Mockingbird is that pursuing the ethical or moral path is never the easy task; it takes a great deal of bravery.

In Chapter 11, Atticus defines bravery as doing what you know is right when you know you'll fail, even "before you begin," and keep pursuing the task "no matter what." He further asserts that when pursuing the brave course of action, you "rarely win, but sometimes you do." In addition, Atticus acknowledges that doing what is morally and ethically correct is always the hardest task, the task one rarely succeeds in, just like he did not succeed in acquitting Tom Robinson due to the racial prejudices of Robinson's jury. Therefore, Atticus also equates pursuing the moral and ethical course of action with bravery.

We especially see Atticus equate moral and ethical actions with bravery when he explains to Scout that just because the majority of the town disagrees with his decision to put his all into defending Robinson does not mean that doing so is the wrong course of action:

The one thing that doesn't abide by majority rule is a person's conscience. (Ch. 11).

Hence, in upholding the ethical and moral choice of action to defend Robinson, despite minimal chances of success since so many people oppose his action, Atticus is also pursuing the brave course of action. Through Atticus's brave and moral actions, author Lee shows us that behaving morally and ethically often requires bravely fighting against the rest of society, and chances of success are generally slim.