One thing in common between LE and OSMC is the connman network manager. Google DNS should not be required.
The best I can suggest is running "touch /storage/.config/debug.connman && reboot" then "journalctl --no-pager -b -0 -f" to tail the system journal and look for issues being reported. Connman debug logging is VERY verbose, but also human readable. Delete the debug.connman file and reboot to revert the logging state.