Alternative to "lossily compressed"

It does feel a bit unnatural, because it is a bit of technical jargon. Audiophiles and others who understand compression will recognize it readily, and to them it will probably sound just fine. The only alternative you have is to reconstruct entire phrases, with possibly disappointing results: Is "processed using lossy compression" better than "lossily compressed"? I doubt it.

There's more than one way to compress a cat.

Since lossy refers to a loss of information, you could call it entropising compression, although that is a word I've just made up, but basically it means making more entropic. Probably not your best bet.

Since lossy also means dissipation of energy you could turn that to mean dissipation of information without too much trouble, and then you could use: dissipatingly, dispersively or disintegratorily(sp?).

I would understand you if you said lossily.