I subscribe to LR CC and am up to date with all updates; so am surprised to find the list of Canon lenses for profile correction is a bit short. For example I am using the 100-400 mk II and there's no profile for mk I or II. Searching here I find references to downloading an Adobe Lens Profile Downloader but for a subscribed service the information on the download page I thought very poor. Given is is subscribed why would you need a customer need to download a profile for a Canon not third party lens that's now in it's second generation. There are also references that I found about community created profiles - that to me sounds really amateurish. So now it sounds like my subscribed and out of date service (since I can't find for mk I of the lens) is wanting me to down load that someone in the community has produced - not Adobe themselves who I am paying. Plus if a profile a user has created is good why isn't it then added to the updates. I just expect a lot better.
The list of profiles is just 13 Canon lenses and I am sure there's at least one missing that I had previously.
I may have missed something - please tell me if I have.
You are seeing only a few lens profiles because your current image is a non-raw image (not an NEF), and there are very few lens profiles for JPGs (or TIFs or PSDs).
Once your current image is a raw file (NEF or DNG from NEF in your case) you should see the full set.