Don't tether directly into LR...it's a joke. It'll go into power save at some time, then not respond and all kinds of other crap that'll drive you nuts. The issue is that Adobe used a really, really old version of the Canon SDK to control the cameras.
There are 3 ways to tether successfully...
1) use EOS Utility and plug your USB in, have it save the captured files to specific folder. Then, in LR, use File->Auto Import and watch that folder. EU will work successfully, save the image, then LR will see it, import it, and delete it from the "capture folder"
2) use Breeze Systems DSLR Remote Pro to do the capture to a temp "capture folder" and import into LR like in #1. DSLR Remote Pro gives you some more functionality that is nice if you are doing studio work...
3) if you have network capability (wifi or wired) on the camera (as the 1Dx does), set the camera to FTP to a folder somewhere on your network (you can install the Windows/Mac FTP server or most NAS's will have an FTP mode). FTP to that folder directly from camera. Then, map that folder as a drive on your LR computer and use the Auto-Import on it. Proceed as in step 1.
I personally tether a lot, and I don't use USB, it's too unreliable as it has to sync correctly. I use the FTP method, as it can be in the middle of a download from the camera to the FTP server and lose the connection. It'll stop and restart the transfer when the connection comes back up (plus, gigabit can go a lot further from the editing computer than a USB with extender).
The other thing about doing it this way is that you can actually have dozens of cameras on the network firing into that folder and one edit station to work with the incoming files.
I've done this in the past with the 1D series at events - save to both cards on camera and with the Wifi attachement send the files to a "remote location" (NAS on private network, hidden under a table with Ubiquiti AP) that is being culled by an assistant on the fly.