I have never been asked to submit actual, physical lesson plans at any public institution in China, I have on occasion been asked to give a lesson outline, IE what I plan to teach over the course of each semester, but that was just a case of writing week 1, Introductions, week 2, random topic etc etc ad infinitum.

Yes, actual lesson plans could be plagiarized, I found out very recently someone has used my name without permission on the internet, and claimed some research I did as my own, in a pamphlet....so yes, be careful.