Hey there! What I do on Linux is use the Thorium browser to make the Apple Music an app in the OS. It works really well, but does have some weird visual glitches every now and then. I chalk that up to me having an NVIDIA GPU and using Wayland though, so it could work better for you!

As for lossless, I am not sure on that as I don’t have ears that can tell the difference so it has never been something I focused on!