While Dropbox can sync files between computers in the same local network, this sync still requires an internet connection to Dropbox.com which handles what will be updated.


Skywatcher wrote:

If I'm not mistaken, Dropbox allows you to sync over local LAN
network. So any app that can use Dropbox for data storage would work in
your situation.
See https://blogs.dropbox.com/tech/2015/10/inside-lan-sync/