I don't know Lanier's specifically, but I just took apart a tape player today, and the motor drove two mechanisms, one for fast forward and reverse, and the other for playback. Each mechanism was driven by a small, black rubber band. In my player, the one that drove the playback had cracked (and the other one probably isn't far behind). My guess would be that the ff/rew band has broken in your player.
I tried replacing the band in mine with a plain old rubber band, but it was too stretchy for accurate playback (it sounds 'wobbly'), but it might work fine for the ff/rew.
Good luck!
Kurt, March 2007