Do I need to include citations when writing my own lecture notes, if I make them public?
First, I think we should maintain good standards of ethics and scholarship for all public/published documents, regardless of whether they've been through peer-review.

Thus, even for "standard" material that's visible in many textbooks, it is "fair play" to acknowledge what you looked at to inform yourself. Indeed, this bit of information does also impart something useful to potential readers.

So, at the least, I'd have a bibliography, and, if not constantly citing those sources, at least some bibliographic notes explaining in some further detail how you used them. This could be a part of an introduction, for that matter, rather than putting it at the end.

(While it is certainly true that at some point(s) one can no longer remember where one first saw something-or-other, so it's difficult to give accurate credit, it is still possible to do a bit of historical research to find out something of the origins of an idea...)