This error is caused by Nagios not having access to the folder where it should save it`s PID file. You can change the path for the PID file (and then also fixing the issue) by editing your nagios.conf (usually /etc/nagios/nagios.conf).
Locate the lock_file setting:
And change it to another path, like for example /tmp.
Start up Nagios again and it should be much happier 🙂