I read “perceptually lossless” to be equivalent to “transparent”, a more common phrase used in the audio/video codec world. It’s the bitrate/quality at which some large fraction of human viewers can’t distinguish a losslessly-encoded sample and the lossy-encoded sample, for some large fraction of content (constants vary in research papers).

As an example, crf=18 in libx264 is considered “perceptually lossless” for most video content.