Are a set of lunch boxes and a set of 4-piece sets bought in Lekou store genuine?

There should be no fakes in specialty stores. You can ask the clerk and see how to explain it. I saw my lunch box with a lock, and the bottom of the box was marked as made in Korea, but both the teacups and cups were made in China production base, and there was no sign of "Made in China" at the bottom, but a square transparent printed label was affixed outside, indicating the place of origin of Weihai Lock Plastic Co., Ltd.

I think your 4-piece set is more likely to be made in China (when opening a grinding tool, the word "made in China" should be engraved on the grinding tool, which is quite technical. No lettering, simplifying the work and saving the cost).