Changing wallpaper from lock screen isn't working.
Make sure your phone is locked. Tap and hold the screen but make sure that you DO NOT unlock the phone with face ID. Once the screen says unlock to edit at the top, tap and hold again. Then the screen should say face ID or enter password as shown in the pictures below. Now it would be okay to unlock the phone. Hopefully that works and you can change it. This doesn't fix the problem when the phone is unlocked unfortunately.
iPhone 7, iOS 15