What type of photos are you trying to import. Pure iPhone shots or other types imported via connection-kit.
How much free storge do you have on you iPhone? Have you tried to reboot you phone. It could be that your phone is running low on memory
These are native iPhone images, as far as I can tell. The only other images visible on my phone have come in though photo stream.
About 2 gig free on my phone: Capacitcy 27.4/ Available 2.0
I've been rebooting and reinstalling several times.
Could you try the import after a "Delete Data" via Lightroom Preferences->Lightroom Mobile and a resign-in.
When you add new photos to your mobile device, Lr mobile needs to import the photos locally and send previews+metadata to the back-end. It seems that some of this data was not send.
If you still see the issue while processing the import could you trigger a diagnostic log.
The Lr Mobile app log can be triggered when you open up the settings and long press the to LR Icon a diagnostic log will be generated and attached to your local mail client.
Send me a LR Desktop diagnostig log - best as a private message with a downloadable dropbox link.
You can trigger the log via LR Desktop prefereneces -> Lightroom Mobile and when you hold down the alt key you will notice a generate diagnostic log button