What happens when you try?
What version of Lightroom?
What operating system?
I click on 'import' and the bar top left starts to show a bit of white bar, as if it's importing, then just freezes and it shows "Importing files..." on the screen. I end up cancelling the import and quitting LR, I have LR 5 v5.7, iMac OS X Yosemite,
If the card reader works, then in all honesty skip the camera connection. The card reader is faster, less error prone, and does not drain the camera's battery.
Bad news here, the card reader option doesn't work now!? so it must be something to do with Lightroom 5 and it's importing settings? what if I completely uninstall and reinstall my copy of LR?
*Just had a thought - it might be the card, will try a different one tomorrow......