I have a document that is divided into parts using manual breaks and page styles. With these, I can turn on page numbering for the different parts independently.
However, I am not able to achieve this for line numbering. What I’d like to have is a first part without line numbering, and then turn on line numbering for the part that follows after the “manual break”.
Is there a way to achieve that?
I assume that your first part is the cover page plus other pages like TOC, copyright, legalese, … which are not really part of the document topic.
Create dedicated paragraph styles for this initial part (in case you also use the same paragraph style in the topic part; otherwise if the paragraph styles are used only there, just customise them). In the Outline & List tab of these paragraph styles, untick Include this paragraph in line numbering box in Line Numbering section.
I realize there is this possibility, but this seems very awkward. It basically means maintaining two copies of the styles.
I think there should be options for line numbering that are similar to page numbering. For example, it would be good to e.g. be able to re-start line numbering for different chapters.
Not, when you use the Parent-Child relation between the two verisons of the styles. Then all of the changed propeties of the Parent style will be inherited by the Child style - except the numbering property, what is enforced differently in the Child style.
I understand, but this still requires me to duplicate every style. It also means setting an option in the wrong place. The line numbering should (for my application at least) be a feature of the part. Because that cannot be done, I’d then have, throughout the entire part, have to use “Header 1-linenumbers”, “Header 2-linenumbers”, “Default-linenumbers” etc, and in the other part “Header 1”, “Header 2”, “Default” etc. I really like LibreOffice and think a lot of things are done better than in Word (e.g. have the page format under “Format” instead of “File”), but this is something where I think the solution with the sections in MS Word makes more sense.
You are possibly right.
But what is your expectation? That you ask fellow users here (this is a user-to-user help site) “how can I do this task”, get a response “it’s possible this awkward way”, and reply “no it should be implemented differently?” 
Please file an enhancement request. New “show line numbering” property for sections looks reasonable IMO, similar how we have columns configurable per-page style and per-section separately.
Note that there’s tdf#112616, but your enhancement would be a more general thing, that would include that in See Also.