error: error creating state file /var/lib/logrotate/status: Permission denied

Are you sure you run this command as root...? ;) If so please check if there is an AppArmour on the system - if yes check it's configuration or uninstall it (Ubuntu case).

DO NOT chmod the default status file to 666. If you chmod it, every user on the system is able to use logrotate as attack vector.

Just define a (private) state file for your user (Assuming that you are trying to run it as regular user) with option [-s|--state file].