I spent the last two hours trying to figure this out. There is a simple explanation that I found by clicking the question mark in the window where the lossy/lossless options SHOULD be.
Apple requires that you be a subscriber for $9.99/month for this option to show. This is really a rip-off. If I download a song after paying for it, I should have the option of getting lossless or compressed regardless if I am a monthly subscriber or not. All other music purchasing platforms that I have experienced give the option for a range of lossy and lossless formats without requiring a subcription.
Because I want only lossless music for my work, I will not be downloading from Apple again- it's a shame- not a wise choice on the part of Apple. I really hope they change this unfair and unreasonable situation as doing so helps artists and Apple Corporation and discourages illegal downloads.
Here is the note from Apple discussed above:
Download (Audio Quality)
Choose the option that works best with your computer, headphones, or connected speakers when playing downloaded songs.
Note: This option appears if you’re signed in as a subscriber to Apple Music.