I lost my Iphone

If you logged into Find My iPhone and can see the device listed there, then you activated Find My iPhone in iCloud. The fact it is offline could be for any reason, but you mention it is turned off. That would be one of the reasons. The decision to lock or wipe the phone is up to you. If you send either of the commands, they will be executed the next time the device is powered up and connected to the internet.

The device wouldn't show a location if you had not attempted to view a location anytime in the past. I don't know that I would say everything is safe. You can take a look at this support document if you want some suggestions on what to do since your device has been lost/stolen. If your iPhone, iPad, or iPod touch is lost or stolen - Apple Support

If your phone is powered off, you can do nothing to it remotely. You cannot track it, remotely lock or erase it. To do anything, it needs to be powered on and connected to the Internet by either a wifi signal or a cellular signal. You need the "offline" indication to change to a location indication before you can do anything remotely to it at all.

And until or unless it does come online, there is no way to know if you did or didn't. You can set up the message to activate, but you cannot know if it works until it actually works.