In my band's sort-of demo (long story), there's a song wtih a keyboard intro that is not transparent with LAME:

FLAC
MP3

Encoder: LAME 3.96.1 -h --preset standard

EDIT: I could have sworn I heard a difference, but repeated attempts to ABX have failed. Kick me off the forum right now, I broke #8.

There are very audible problems at lower bitrates, however. An ABX at --preset medium got 10/10, p .01, and in the -V6 encode of the song I have on the band's web site, the artifacts are very annoying. I usually can't ABX --preset medium and -V6 is usually unnoticable without direct comparison with the original.