My daughter had this problem today.
Phone died, plugged in the charger, waited awhile, booted up phone, started optimizing apps, rebooted, optimizing, rebooted and so on.
The Life One X is the slowest charging phone that I have ever seen. Lollipop is notorious for optimizing apps on reboot and the process can take a long time.
The minimal charge on the phone was insufficient to finish optimizing apps. Battery died. As it began charging again it started optimizing apps. Battery died. Repeat.
I tried several things and finally got it to charge without rebooting.
I plugged it into a 180mA charger for a Jabra Bluetooth headset. (Yes, 180 mA.)
It charged for 15 minutes without rebooting. I then plugged it into the charger from my Nexus 6. After an hour it had a 25% charge.
Can't promise that it will work for everyone, but a trickle charge worked for us.
If you don't have a real low mA charger, try plugging it into a USB port on a computer.
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