While I would really have to learn more about the type of VPN and the configuration, in general I would say “no”.
Usually, a VPN client would go to an outside IP address and that IP address wouldn’t be accessible from the inside LAN.
Also, the question that comes to my mind is “why would you want to use a VPN client inside your LAN”? It would just slow down the transmission because of all the encryption and, hopefully, your internal LAN is already secure.
I hope that helps.