It seems that the fatty acid profile for cheeses varies (and can be varied through manipulation). Whether a cheese is made from sheep or cow milk will effect the profile and what the sheep/cows are fed will also effect the profile.

I found this pdf file giving a breakdown on both sheep and cow milk fatty acids: Dairy Pipeline - the table is on page 4.

Chevi, the 'technical definition' of a hard cheese is one with 26-50% humidity/moisture and includes Cheddars, parmasan, and swiss.

Mayo is a LC food (it's mostly fat) - you can find a pretty decent list of LC foods that are recommended for a CKD at: http://www.cythrawl.org/ketosis/howto/cancanteat.shtml

HTH
Nat