At first I thought "Auntie! Auntie!" was Lily trying to catch the attention of her relative.
Then I realized it's the yuriworld's version of "Uncle! Uncle!" 
Actually, I think it's Lily being unrepentant about what she concerning her cousin's actual age despite the physical abuse she's suffering, because the Japanese word for "aunt(ie)", obasan, also has a connotation of "old woman" (probably due to high similarity with the word for "grandmother", obaasan).