'Etiquette' of including course lecturer as author in a paper Consider please the two following cases:


I took a graduate course, and I naturally did the final project on something related to my research subject. I got a nice conclusion from it. It wasn't nearly enough for publication, but I later on wrote a paper that had included material I got doing my course project. The 'size' of contribution (if that has any relevance) was about half a column from the entire paper. The course lecturer hadn't helped me especially, i.e. we didn't remotely discuss publishing anything.
I did another graduate course, in which the lecturer talked about his own research. Later on, unrelated to the course, I used the methods he taught and wrote a paper based on it.


These are two unrelated cases.

I was wondering if the lecturers should be included as authors in a paper in either case.
Authorship is reserved for people who contribute to the scientific output of the article. It is not clear to me that the cases you mention qualify although they could. The Vancouver Protocol (here as given by the ICMJE) provide a good basis for assessing authorship. If your course lecturer fulfil these criteria and thus actively participate in the creation of the article then all is fine. If the lecturer takes no active part then the appropriate way would be to place a note in the acknowledgement of the contribution.