Hi caity_lynn,
We appreciate you reaching out through Apple Support Communities for help with your iPhone and setting a Live Photo as your wallpaper. We'll get you pointed in the right direction.
So that we're on the same page, what's the iOS version installed on your device? This can be found under Settings > General > About.
Have you had an opportunity to restart your iPhone since noticing this behavior? If not, let's do so now. Here's a guide with the steps for a standard restart:
Restart your iPhone
We'd also like to share the information in the following guide under the section titled, "Set a Live Photo as wallpaper for the Lock Screen" for help setting a Live Photo as your wallpaper:
Change the wallpaper on iPhone
Have a great day!