Actually the cat didn't. I spoke to her over and over nothing happened. I finally found it hiding in the shadows on floor 1 of the dungeon.
Its right by the secret room too, but as dark as that dungeon is and it being on the other side of a poison tile I never saw it as only its paw barely glanced the light radius.
I do think there is something off on that event though as the cat never left Sarah, I got no prompt it was gone ever. All that happened was I talked to the cat, it now lived with Sarah. Then I fought a boss and the cat ran off from the party (but was never IN my party to begin with, so that was odd), and Lexus refused to ever talk to me. I could spam it over and over, nothing. I even went back to town and the cat was still with Sarah, nothing was happening.
I finally then found it on floor 1, it ran to secret room 3 I found it there, then talked to Lexus and the game progressed. Though I am confused as how did the cat get here if it never left Sarah and there was no scene for it?