The Atticus example is, as Murphy said, a pure conditional sentence because it is an answer to the question "Why, then, do you think he agreed to defend Mr. Robinson?" The answer cannot mean "Even though / Despite the fact that he lost..." because the answer, like the question, needs to refer to a hypothetical future: he agreed to defend Mr. Robinson because "even if he lost / were to lose..."
I disagree that you can't use 'despite' here. Here is the passage in full:
'Why, then, do you think he agreed to defend Mr Robinson?'
A boy in the back raised his hand.
'He wanted to make a difference.
Even if he lost, if Atticus could make one person start thinking differently about racism, then he made a difference.'
In my opinion, 'despite' functions perfectly here without obscuring the meaning:
'Why, then, do you think he agreed to defend Mr Robinson?'
A boy in the back raised his hand.
'He wanted to make a difference.
Despite losing, if Atticus could make one person start thinking differently about racism, then he made a difference.'
If you wanted to retain the 'even if', the sentence would sound better if it were reworded as follows:
'Why, then, do you think he agreed to defend Mr Robinson?'
A boy in the back raised his hand.
'He wanted to make a difference.
Even if he were to lose, if Atticus could make one person start thinking differently about racism, then he
would have made a difference.'
Maybe I'm wrong, but this is what sounds natural to my BE ears!

The third sentence ('even if he were to lose...he would have made a difference') is my preferred one.