I came up with a theory. that I literally came up with whilst taking a shit

Lillies symbolise purity and beauty. "Lille" is a corruption of "Lily", therefore, Lillie is the corruption of purity in Alola.
"Hau" means "snow" in Hawaiian, which is often attributed to purity as well. Hau is the one to put a stop to Lillie's corruption.

Lillie is also Kukui's assistant, who studies pokemon attacks. Lillie is obviously using this to get to Solgaleo/Lunaala and their attacks that disregard abilities to corrupt Alola