The encoder matters a lot. A Xing-encoded MP3 is painfully obvious even at 320kbps, but LAME is extremely competent already at 128kbps.
I've been able to ABX 320kbps LAME MP3 against the lossless source, but only by repeatedly looping very short (1s or less) sections and quickly switching between A, B, X and Y in order to pick out a very isolated reverb tail or resonance or something similar.
I sure hope nobody actually listens to music like that for pleasure!
It was a while aho, but IIRC it was a solo harpsichord recording (which is a know problem for MP3, along with castanets) and it was more a subconscious thing than something I could actually put my finger on an identify. I could never even come close to hearing a difference when actually listening to the music, and not just isolated sounds.
All of the more modern codecs (Vorbis, Opus, AAC and so on) are absolutely 100% transparent to me, at much lower bitrates. For my phone I use Opus at 128kbps, and even that is overkill with a decent amount of "just in case" margin.