I have a sort of laundry list of ideas about ways to resolve this.
Most likely issue
The ICC profiles of the images you are trying to import are broken, or marked as "Uncalibrated". Lightroom is having trouble determining exactly what they are, so they need some type of profile embedded before they can be imported. You should be able to open the images in Photoshop or Gimp and embed them with sRGB or similar, then Lightroom can import them without any issues. More info can be found in this thread.
Other potential solutions
It is possible that another application such as iPhoto, iTunes, or Windows "Import Pictures and Video" has the files/folders locked on the iPhone. I would suggest doing a full sync with iTunes, then closing iTunes completely before opening up Lightroom.
I am also wondering what status your iPhone is in, are you in "syncing" mode that was common prior to iOS 5 or are you already disconnected? This would be something to think about if you have an older version of the iOS installed.
Another thing to look at is what type of files you are actually trying to import. It is possible to create all kinds of image files that are not compatible with Lightroom, using apps on the iPhone. Certain image types will appear in Lightroom as "importable", but not give you a preview because they are not fully supported file types.
Example of what you may see with an unsupported file type:
Finally, if you want to try something further, I have read accounts that the following may work:
Lightroom Preferences > File Handling tab > Camera Raw Cache Settings > Purge Cache