It is not clear what you mean by 'AE 6 CC'.
Cinema 4D Lite is included with After Effects CC (12.0) and later.
Details are here:
Sorry, I was wrong; I only had AE 6. I have now updated to AE 6 CC, and it
works fine, thanks.
Again, I don't understand what you mean.
After Effects CC is version 12.
After Effects CS6 is version 11.
I presume that you mean that you are using After Effects CC (12.0) or After Effects CC (12.1).
I have version 12 loaded, and it works, thanks.