Computer hardware and software can go wrong sometimes! When your router software is failed or an application in your iPhone is failed. Your iPhone LTE could be still On even if the WiFi is connected!
Two ways to fix this issue. First way, turn off your router power and turn it back on again. It may fix your problem.
Second way, check your iPhone firewall if you have a firewall installed. Make sure your firewall does not block the WiFi connection.
Double check your VPN, make sure it is On. If it is Off then you are likely not connected to WiFi!