The "h" before "uair" is not lenition, but rather a means to distinguish the vowels (and at the samet time the two words) "a" and "u" in two consecutive words from each other. As cén ends in the consonant "n" there is no need to place anything else inbetween.
(WHY?? Well you know the Irish pronounciation with many vowels together may get confusing, such as e.g. "aoi" in "daoine". It could be fun thoughj trying to figure out how to pronounce the construct cáuair ;- )