They really are short videos, not image files. If the iPhone created two files, the preview video and the image file you could delete the preview video, but I don't think the iPhone does this. In any case the solution lies with the phone, not Lightroom.
This issue was corrected in LR CC 2015.9 / 6.9. So your options are:
- Upgrade to LR CC 2015 or LR 6 (costs money).
- Use the Image Capture program on your Mac to transfer the photos from the phone to your Mac hard drive. Using the Finder, delete the videos. Then import the photos from there into LR.
- Use LR to import the videos and photos. After importing, select the videos and hit Delete; click Remove (not Delete From Disk). In the Finder, navigate to the folder containing the videos and photos; delete the videos but not the photos. Import the photos from there back into LR.
IIRC they are called Live images and as stated above are videos. So stop using the Live Image (Live Photo, or whatever it is called) option (that is if you can turn it off).
Thank you John. This is very helpful.