How come this is not a run on sentence?

No, it's not a run-on sentence. The ideas of the two clauses are related, and it is not unreasonable that they be found in the same sentence.

Perhaps it's the word "where" that makes it awkward.

May I ask you a question if we are to get the book needed?
May I ask you a question when we are to get the book needed?

Of course, the original could be re-worded:
May I ask you where we are getting the needed book?

Punk you've probly been advised already, but

...seems to ask whether he might be allowed to speak up in the event we receive the needed book

Maybe "from where" or more snooty, "from whence"

I would say

I'll ask you a question: where can we get the book we need?

Informally, one could use a dash instead of a colon.

Best yet

Perhaps it's the word "where" that makes it awkward.

May I ask you a question if we are to get the book needed?
May I ask you a question when we are to get the book needed?

I gave those as samples of OTHER words, rather than "where," that might be used in the sentence. Of course they change the meaning. Sorry for the confusion.

Jesus wept, what a bunch of boobs--this is a question from an examination, suggestions on how the author might change the sentence are meaningless. The instructor wrote the sentence and the author here wants to complain about being marked down on the exam. I swear, English language learners' questions seem to befuddle people here, so that they cannot read and understand the OPx.

Again I just want to clarify. I AM an ESL instructor. These are questions brought to me by my students. They don't understand the logic and neither do I. I am here to find answers for them.

Thank you everyone! It's been most helpful!

Are these questions from exams other people set?

Is there another instructor there who can help you with EAL/EFL grammar questions?

These are from the official High School Examination, which is one of the most important exams in China. So theoretically these questions should've been written by grammar experts. Although I can't change the exam, I still would like to know whether these questions are indeed grammatically correct. Some of the questions "sound" wrong to me, but I can't explain why. And it may very well be that I am wrong.

I think what's interesting about exam questions is that they seem to use very awkward sentences that are probably grammatically correct. Sometimes students would point to another answer and ask "But teacher couldn't you say this sentence this way too?" I am tempted to tell them that yes, you can say that in informal speech, but I don't want to misguide them or tell them, "Actually your teacher snoozed through most of grammar class during middle school." :p Hence I am here seeking help. And to relearn proper grammar.

I suspect your intuition is exactly correct.

Well, i explained the logic to you. The two clauses of the sentence are related, and there is nothing illogical or ungrammatical about combining them in a single sentence. My apologies for assuming that you were a disgruntled student. We do get students in here who seem to hope that they will be given an answer with which they can confront their instructor.