Sourcing lecture notes instead of publications
I firmly believe that one should cite what one has used... and possibly more. To use a source and not cite it is simply dishonest and fails to give credit where it is due. At the same time, yes, one also wants official credibility, which usually entails citing refereed-journal publications (although the latter is not a promise of correctness, either). If nothing else, citing refereed-journal publications is expected, so doing it is doing what one is expected to do.

(Lecture notes are not always mere echoing of textbooks or journal articles.)

So, cite both the actual source you used, and find "cite-able" sources to accompany, so you'll be both honest (and explanatory) and "formally correct".