You can control the animation of your Live Photos using some smart effects in the Photos app.
Snap a Live Photo, then find it in your Camera Roll. Open up the image, swipe upwards, and you’ll be presented with several options.
These are Loop, which means your Live Photo will loop its clip over and over. Where possible, it tries to make a seamless loop by merging the beginning and end of the clip. iOS then puts this image into the Animated smart album.
Another option is Bounce. Selecting this means when the clip reaches the end, it will then bounce back the other way and run the clip backwards. This will also loop infinitely.