It supports Lossless, just not Hi-Res. Full stop.
Support page provided was for the Apple Music app's casting function, not about Lossless audio in general. And ALAC of course stands for 'Apple Lossless'.
You can play the Lossless audio and send it from the system output, though. AirPlay via the source operating system is usually capped at 44.1k and the ATV then upsamples to 48k for either HDMI or optical output. I think the ATV 3rd gen app is a mix of Music and iTunes, but it was broken for me, like they just abandoned it.