It's a telling story that Keith Bradford relates. "Would" leaves a lot up to interpretation and context. In making denials, it's less strong than saying you didn't do something.
The idea of a moral stance here doesn't derive solely from "would". It also derives from the context of the activity mentioned (lying) and the denial.
We could use the same basic construction with a different activity and possibly intuit different motivations for the speaker:
"When I was a child I wouldn't brush my teeth." (meaning: I routinely refused to brush my teeth as a child, I was a stubborn child. To refer to a habit I would say it differently: "When I was a child, I never/rarely brushed my teeth." Or, "I wasn't in the habit of brushing my teeth as a child.")
Another example:
"Even when I was working on the tenth floor of an office building I wouldn't take the elevator, I always took the stairs." (Meaning perhaps: I'm dedicated to getting exercise wherever I can, and so I always choose to take the stairs. But, it was also my habit to take the stairs when I worked on the tenth floor).
So what is habitual and what we choose (or are willing) to do, or not do, sometimes overlap. With lying or arriving late I hear it more as a moral choice. But context matters, so I wouldn't state this as an absolute. Just that, as a native speaker, if I wanted to talk about my habit of arriving on time to class, I would probably find another way of saying it to avoid ambiguity or uncertainty:
When I was in school I always got to class on time.
I was very punctual as a student.
However:
"I wouldn't arrive late to class..." This construction by itself introduces ambiguity, something unexplained and therefore confusing without more context.
You
could say:
Even when it was raining and I hadn't had a good nights' sleep, I wouldn't arrive late to class.
Now we can understand the "wouldn't". Here it clearly refers to a habit, and it makes sense because we are told what the condition is that "would" refers to:
"(Even if it was raining and I was short on sleep), I wouldn't arrive late to class."
Otherwise, I would stick to a positive construction like the ones I gave above.