"There is no man who has never looked upon a woman WITH/WITHOUT desire"

If we parse from the right beginning with "has never looked at a woman with/without desire" and apply it to an individual man, call him Mark, then

Mark has never looked at a woman without desire

means that Mark desires every woman he sees.

Mark has never looked upon a woman with desire

means that Mark is not attracted to women.

The left part of the sentence "there is no man living who" tells us that "Mark" does not exist.

So either Atticus is saying there is no man who is a total nymphomaniac, desiring every woman he ever sees (the "without" meaning); or Atticus is saying there is no man who is un-attracted to at least one woman(the "with" meaning).

Neither of these really make his point. So parsing from the left is the only way to make a meaningful expression, and this is probably the most natural way to do it anyway.

"There is no man living who has never" is identical to "every man living has, at least once". in most cases men look upon some women with desire and others without. Every man has looked at a woman without desiring her. Every man has looked at a woman with desire. However, only "with" makes the point Atticus was making. Every man has, at some point, looked upon a woman with desire.

The correct version is

and there is no man living who has never looked upon a woman with desire.

but in rhetoric, as opposed to logic, both ways would be understood.

The phrasing is probably based on Matthew ch5 v28

But I say to you that whoever looks at a woman to desire her has already committed adultery with her in his heart

I don’t want to pick on anyone in particular, but for clarity’s sake, I have to point out that Lawrence has it backwards. With the “without” version, what Atticus says can be expressed as

~ ∃ x (M x · ~ ∃ t ∃ y [W y · ~ L x y t])

where

M x means x is a living man;

W y means y is a woman;

L a b t means that a looks on b with desire at time t.

If we minimize the scope of the negations, that expression becomes:

∀ x (~ M x ∨ ∃ t ∃ y [W y · ~ L x y t])

or

For any entity, either that entity is not a living man, or there’s some time when there’s some woman whom that entity (man) does not look on with desire

which is true, but, judging from the context in the novel, is not what Atticus meant. I suggest that the “without” was to begin with a typo.