So assuming that you’re looking at upgrading from 2.0.7 to 3.0.x or 3.1, then you would need a maintenance window as the container configurations have changed and some manual tweaking may be needed.
if you’re just looking at upgrading from 2.0.7 to 2.0.11, then that should go smoothly with no manual intervention needed.
For the switch to 3.0 or 3.1, there is a lxc-update-config tool which can automatically convert most configuration files by just renaming the configuration keys that have changed. You can run that while the container is still running, then attempt to stop and start just one container to see how that goes and if any manual action is needed. If that goes smoothly, then apply the config change to all containers and reboot the host or restart all containers.