With the limited information that you have provided, I had to guess the problems faced by you. Some of it can be understood by reading below
- To save FaceTime Live Photos, all participants need iOS 12.1.4 or later, or iPadOS. Not all features of FaceTime Live Photos are available with earlier versions of iOS. FaceTime Live Photos doesn’t work with iOS 11.
- Are you picking up the Live Photo from Live Photo Album?
- Have you Set the wallpaper for only Lock Screen or Set it for Both.
- Have you tested the live photos as it is?
Set a Live Photo as wallpaper for the Lock screen
When you set a Live Photo as wallpaper, touch and hold the Lock screen to play the Live Photo (on all iPhone models except iPhone SE).
- Go to Settings
> Wallpaper > Choose a New Wallpaper. - Do one of the following:
- Tap Live, then choose a Live Photo.
- Tap your Live Photos album, then choose a Live Photo (you may need to wait for it to download).
- Tap Set, then choose Set Lock Screen or Set Both.
If you still think this is an issue then you may please provide --> Product Feedback - Apple <-- here