Set dropbox to only use LAN sync (dont allow web sync)

What you want is not possible. (There is a workaraound, see below.)

"Lan Sync" only begins to work when the file is uploaded to the Dropbox-servers. There it can be evaluated who can get the file via "LAN Sync".

If you drop a file in the Dropbox-folder on a workstation the file is not yet known to the Dropbox-servers. It first needs to be uploaded to the Dropbox-servers before the transfer via your LAN can begin. After uploading to Dropbox your file if possible will be transferred via LAN to your server (but that's not what you wanted).

Workaround:
The only way this could work (somewhat similar to what you want) is if you share the Dropbox-folder on the server within your network and the users drop files in that shared folder (directly on the server). Then, after uploading it to the Dropbox-server, it will be transferred via "LAN Sync" back to all your workstations.

They just need to know not to use their local Dropbox-folder when connected to the server (because otherwise the local Dropbox begins uploading again). I assume these are laptops who are often disconnected from the network because otherwise there would be no need for the Dropbox-client on the workstation because you already shared it via the server.

Other alternatives that allow for local syncing without the cloud are:

BitTorrent Sync

Device to device. Skip the cloud. Fast, private file sharing for teams and individuals.

SparkleShare

SparkleShare creates a special folder on your computer. You can add remotely hosted folders (or "projects") to this folder. These projects will be automatically kept in sync with both the host and all of your peers when someone adds, removes or edits a file.