Unfortunately no app, including Lookout Life, can work when a phone has no power.
However, you should still run a locate just in case your phone gets powered up again and acquires a network signal (WiFi or data).
A phone running Lookout Life will check with our servers multiple times daily, and if the phone regains power and network connection it can connect to Lookout Life servers and execute the waiting locate—and lock—commands. If that happens, you will get location information and, if appropriate, an update that the lock has occurred in your email.
Unfortunately, it is not possible to power on or re-charge a device remotely. These are limitations in the technology currently employed by smart phones and tablets.
Note: If you have run a locate for your device and are not receiving emails with location information, it may indicate that your phone is powered off or in an area where it does not get a network connection. Please know that if you call your device and it rings, this does not ensure that the device has a data connection.