Could you please confirm the version of Lightroom that you are using and the camera make and model?
Also, make sure that the destination location is set correctly and has full read and write permissions.
The most common problem for "cannot be read" errors is a WRITE permissions problem on your destination folder. (Mac users see this frequently, especially after updating the OS.)
Using Finder, make sure you have READ and WRITE permissions on the import destination folder and its parent.
I had the same problem - new user and couldn't figure it out. Was not working for phone or camera SD card. Searched many postings looking for an answer and in my case it was that the destination folder did not have write permission. The problem was the Default folder was not to the pictures folder. As soon as I changed the destination everything worked! Stupid error though, since it isn't that the files couldn't be read!
how do I change the destination!?
In the Import dialog, right side, Destination panel.
My Lightroom does not give me an option to name my files or set the destination????
What has happened here??
If the Import dialog is only a long, thin rectangle, press the arrow in the lower-left corner to get the full-screen dialog back.