So I think this is actually more of a semantics issue than a translation issue.
school route which is unsuitable/unusual for/during lunch break
I might translate
for lunch break in this specific case, although in most cases
during lunch break is definitely the obvious choice. However, the point I really want to make though is that
unusual for lunch break is maybe not as strange as you seem to be suggesting it is, at least assuming the speaker in this case is a student.
The sentence appears to be saying that this person was called out to an "unusual" place to be during lunch break, presumably in the sense that it's not the kind of place you would expect students to be at that time. This makes sense for a school route; by definition we only expect students to be there in the morning/evening.
A much looser (but easier to understand) translation of the first sentence:
The meeting place was on my route to school, the last place I expected to be during lunch break