Omitted 了 for multiple verbs in sequence
You should use "了" when you are implying an event has happened in reality.

"了" is not about past. It's a marker, rendering verb's result to reality realm. Verbs can be in imaginary state, you know... 

ex: "I would have done that..."

Ask your self: 

"What chinese bare verb mean? How to translate 她在图书馆看书?
Is she reading right now? was reading? will read? The correct answer is : it's all at once!"

The best translation will be using some kind of indefinite forms (maximum ambiguity). Imagine that a freind of yours tells you about a girl: 

"So I walk in and she is like.. reading in the library"

Ask a question about this picture: "Did it take place or will it take place? Are you telling me about factual past or telling me about probable future? Have you walked in and saw her or will you walk in and see her"

Now, about your sentence:
有一天，她在图书馆看书，一个男生从她身边走过，看到她的手套掉在地上，那位男生很有礼貌地帮她捡起来 (no 了, no 就)

The translation should be indefinite in some sence:

"There is a day once, and a girl reads in a library and the other guy passes her by. He sees that she drops a glove, he picks it up."

Do you see the mood here? It looks like a fairy tale of some sort, it's not real. 

Now, if you add 了 at the end, it comes with 就 (since it's a stiff structure here). i.e. 了 is linked with 就 and not with the rest of the sentence, and thus addition of THIS 了 will not render the whole sentence from a fairy tale realm to this world. 

有一天，她在图书馆看书，一个男生从她身边走过，看到她的手套掉在地上，那位男生就很有礼貌地帮她捡了起来. 

Now translation changes a bit: the first part stays the same and we can't tell if it's an imaginive or real situation (took place in the past), but the last part translates like this:

"He sees that she drops a glove and then就 he picks了(for real) it up. (He will do it if situation is\was\will be real"

Now, unless you add 了 to  the first part of the sentence 有一天，她在图书馆看书，一个男生从她身边走过，看到她的手套掉在地上 you can't tell that situation took place or will take place. 
You know 有一天 makes you think that a fairy tale is about to start, so lack of 了 reality makers makes sence! The last 了 is not a marker for the whole sentece but for 就_了 part, there it just stresses logical consequence of the actions (real or imaginary), but it never answers to the question: "Is the WHOLE story a reality or are you imagining things?"