Why is this? Is this normal?
It is not normal. Which version of Photos and MacOS X are you using?
My Live Photos are showing a camera tag and a lens tag. I am using macOS 10.13.3.
Did you edit your Live Photos in an external editor? Quite a few of my photos are using the lens information and other EXIF tags, when I edit them in external editors.
If you transferred the photos by a Shared Album, they may also have lost the lens tag or other EXIF tags.
If you are not running the newest version of MacOS X consider to upgrade and check, if that will bring the camera information back.
As a work-around, you could open the predefined smart albums "Live Photos" and "Animated" and add a keyword "Live" or "iPhone X" to the iPhone photos.
Phots has no tools to add or modify EXIF tags. Whenever some of my photos are missing EXIF tags like camera or lens tags, I am exporting the original and add the EXIF tags with exiftool in the Terminal.
Then I delete the old version from Photos and reimport the modified photos to Photos. For the update to wirk, you have to empty the Recently Deleted album, before you reimport the Live Photo, or Photos will just use the old original.
For how to use exiftool see. Modifying EXIF tags of Originals Using exiftool: camera, lens, gps
These lines will change the the camera tags, if you install exiftool: Just replace $1 by the path to the image file
For the iphonexback camera:
exiftool -overwrite_original_in_place -preserve "-Make=Apple" $1
exiftool -overwrite_original_in_place -preserve "-Model=iPhone X" $1
exiftool -overwrite_original_in_place -preserve "-Lens=iPhone X back dual camera 6mm f/2.4" $1
for the front camera:
exiftool -overwrite_original_in_place -preserve "-Make=Apple" $1
exiftool -overwrite_original_in_place -preserve "-Model=iPhone X" $1
exiftool -overwrite_original_in_place -preserve "-Lens=iPhone X front TrueDepth camera 2.87mm f/2.2" $1