Thank you Igor!

sure, with or without Last-Modified header does not matter with generating unique names for the static artifacts (js, css, images).
But setting Last-Modified header results the browsers send if_modified_since to nginx to check freshness of the files, which are actually unnecessary, cost server processing time.

Setting Expires Header and change name of the files are enough to ensure that the browsers always get the fresh version at the right time. is it right so ?

Again, thank you igor!