for example, could my lucario be paralyzed and asleep at the same time?
It is impossible for a Pokemon to suffer from more than one primary status condition (Burn, Paralyzed, Sleep, Freeze, Poisoned) in all generations. A Pokemon may suffer from several minor status problems (for example Confused or Infatuated ) at the same time. Source: http://bulbapedia.bulbagarden.net/wiki/Status_condition#Non-volatile_status