I can imagine a dolphin-like civilization which lacks money. Dolphins seem to have relatively few goods of value, yet they are highly intelligent and have well-developed emotional lives, or at least they could be so even if you are for some reason skeptical about current-day dolphins.
Current dolphin goods seem to be food, sex, kids, and conversation, with a fairly tight PPF. They don’t buy lampshades. Most of “dolphin economic growth” seems to come from finding more and better food, getting more and better sex, finding safer environments for the children, and learning to enjoy other dolphins more. It’s hard to store dolphin goods and thus it is hard for the Mengerian origin of money story to get underway.
Also covered are bird-like and bee-like economies.