While we have crickets here I never had one in the house. Filou also ate moths and he didn't puke. But I caught him one day with a moth in his mouth that was too big for him. A wing stuck out and it was humming frantically in Filou's mouth- I first had no idea whether he tried to swallow a mobile or something vibrating I opened his little mouth and it flew away.
Maybe Lily ate that thing to produce the hairball