None of the factory head units in the LS, be they base, Alpine, SoundMark, or THX/NAV, will play MP3s. You can burn those MP3s to an audio CD, which will play in any of the CD-equipped units, but then you're playing an audio CD, not the MP3s themselves.
You can buy adapters that will allow you to connect your portable MP3 player to your factory head unit. It's a cryin' shame, IMHO.