Here you will find more information about syncing files between different locations.
http://windows.microsoft.com/en-us/windows-vista/how-to-keep-your-information-in-sync
I would do the following in your case. I would copy folders the network share that need to be synchronized.
Then right-click the network folder and click Always available offline.
http://windows.microsoft.com/en-us/windows/working-with-network-files-offline#1TC=windows-7
Hi,
As mentioned by T. Kujala, you can use sync center\offline files to sync the files. I haven't found a way to only sync when connected to LAN, but you can refer to the following Offline File group policy settings which might do some help:
Computer Configuration\Administrative Templates\Network\Offline Files
Configure Background Sync
Configure slow-link speed
Enable file sychronization on costed network
(similiar in Windows 8.1 system)
https://technet.microsoft.com/en-in/library/ff633429%28v=ws.10%29.aspx?f=255&MSPPError=-2147217396