"Lossless communication" doesn't quite seem to capture what is special about human communication. The difference is more about complexity of communication than losslessness. Being able to communicate using a fully recursive grammar is the key difference. I think that's the concept you're heading towards with "losslessness".

But which came first: being able to communicate using a fully recursive grammar, or participating in a viciously competitive political/social hierarchy and having the resulting selection pressure dramatically increase the size and complexity of our brains over what is, in geological terms, a ridiculously short period of time?