From where are you trying to transfer files? From the local network or from a remote network? Using the word “LAN” generally means one’s local area network.
I have no problems transferring files using the WD My Cloud for Android app on my local network when there is no internet access on that local network. Same goes for ES File Explorer. There is no need to enable FTP (which I have disabled anyway) when using ES File Explorer on my local network or when using the WD apps/software locally or remotely.
With ES File Explorer one may have to manually add the My Cloud on the Network page in the app. The following example shows how I have the My Cloud entry configured in ES File Explorer on my Android devices.
Remote access is a different story. For remote access typically one would either have to use the WD apps/software, MyCloud.com web portal, or enable FTP and do port forwarding (of port 21) within their local network’s router/gateway. There are possibly unofficial methods of remote access but currently the previously mentioned ways are the official methods.