The Good:
-Kha chases his desires. He wants to become the ultimate predator by devouring all in his path. Illaoi's religion promotes this, Kha is in motion.
-Kha isn't undead. He can die and follow the flow of the universe, as shown when he fought Rengar in his lore.
The Bad:
-Kha is from the void, which Illaoi views (along with voidkin) as "designed by fools" based upon her views on Rek'Sai, so she might not be fond of Kha'Zix in this regard.
Would Illaoi hate Kay-Z?:
Yes and no. Kha doesn't break her religion's rules. He chases his desires in life and will die shall the time come unlike someone like Thresh. However, she might have a prejudice towards Kha and the rest of the void because her God doesn't control them. They are made by someone or something else that is not Nagakabouros, so she is wary of them.