I understand you are experiencing issues with setting a lock screen wallpaper. If you haven't already done so, you may want to restart or reset the iPhone:
Restarting your iOS device
1. Press and hold the Sleep/Wake button for a few seconds until the red "slide to power off" slider appears, and then slide the slider.
2. After the device has turned off, press and hold the Sleep/Wake button until the Apple logo appears.
Resetting your device
If your device stops responding, you can reset it by pressing and holding both the Sleep/Wake and Home buttons for at least ten seconds, until the Apple logo appears.
If the above does not resolve your issue, the next best step will be to restore your iPhone using a computer with iTunes. Please be sure to backup your iPhone first.