Thanks for double checking the steps and testing other Live Photos. The next step is to reinstall the iOS using iTunes.
Please make a backup of your data prior to doing this step: You can make a backup in iCloud or iTunes using this article: How to back up your iPhone, iPad, and iPod touch
Once your data is backed up, you can reinstall the iOS using this help article: If you can‘t update or restore your iPhone, iPad, or iPod touch
Please pay close attention when you reach step 4 which says:
When you see the option to Restore or Update, choose Update. iTunes will try to reinstall iOS without erasing your data. Wait while iTunes downloads the software for your device. If the download takes more than 15 minutes and your device exits recovery mode, let the download finish, then repeat these steps.
Once your iOS is reinstalled, test if the issue with your Live Photo on the Lock Screen is still occurring. Thanks again and have a great rest of your day.