IMHO lossy/lossless feels like the wrong term to use for natural-language text.

Every time natural-language passes from one human to another whether verbally or in the written word, there is a greater than zero percent chance that the meaning will be received/understood in a way that is "lossy" compared to the communicating party's intent. The so-called "telephone game" is a very good example of this.

It seems true that the lossy problem arises even without any LLMs or any intentional transformations.

Lossless in other domains basically means perfect-fidelity carried across copies. Natural language seems almost incapable of this ideal.