You could edit /etc/resolv.conf and specify a public DNS IP there (like google's 8.8.8.8 or cloudfare's 1.1.1.1) that will restore your connectivity.
Check out discussions in this post:
All you would need here would be the IP of Pi-hole.
One thing you need to make sure is that you set-up your Pi-hole installation to the correct interface (eth0) and from the admin interface, you set up the listening behavior (in your case ) to listen to all permit all origins.
That way both the LAN devices and VPN will go though Pi-hole.