"Lossless flac" is indeed compressed, meaning smaller than PCM WAV files. May not be lossy, but it IS compressed.

And yes, CDs carry digital audio, but it is a specific format that needs to be converted to whatever format you use, be it WAV or mp3.

But saying CD audio need to be "digitized" is a effect of media and public stupidity, to us audio engineers. The great unwashed (meaning non-engineers) thinks making an mp3 is "digitizing" :-)