The fact that the nagios.lock file is missing usually just indicates that nagios isn’t running, as that file is created when Nagios starts and deleted when it stops, to prevent multiple instances of Nagios being run, methinks. This is why, if Nagios is stopped and you try to restart it with the startup script provided, it will give you that error, but it should then go on to start Nagios for you.
Now that Nagios is running, go to your nagios/var/ directory, where the lock file is by default installed, and confirm whether or not it is there. If it’s not, check your config files to see where Nagios is configured to create that lock file, and then go there. Let us know what you find out.