When I download Canon .CR2 files from my 7dII LR is extremely slow and many files are shown with corrupted areas of bold color blocks instead of the image. I've repaired LR via a fresh download. Canon's DPP file viewer shows the files normally. I originally thought it was defects in my CF and/or SD cards, but it is happening with all of them.
DPP is only showing you the built-in preview until you try to create a JPG from the CR2, then it’ll actually use the raw data like LR is. Test by creating a JPG from one of your CR2s in DPP and see if you get an error.
If you feel LR is not transferring the files well, then just use your OS to do it, copying from the card to a place on your internal drive, first, then do the import from there, that way LR and the card aren’t both being used at the same time.
The files were fine, I did the test you suggested with DPP and had to do a fix on LR5, including a "trash preferences" and now it's working OK.