How do I know what a lossy compression process removes from the original ?

Its pretty hard to determine but if your savvy enough with audio editing tools like Cool Edit it can be done. The process goes like this. You take a compressed and uncompressed version of an audio track and mix them together out of phase with each other. What this does is cause all the information that is the same in both tracks to cancel itself out.  If the two signals are identical  they should cancel each other out and the sum of the two signals should produce silence. Any signal that is produced is the difference between the two tracks, or what was missing from the compressed version of the track. You can measure or listen to these compression artifacts in difference signal to hear what was removed in the compressed version of the track. You will notice that as higher compression ratios are employed there are bigger differences between the two tracks and this difference signal will increase in amplitude or volume and change in pitch or frequency.