You would probably choose one of these examples if you wanted to say that you got up behind of schedule:
Je me lève tard. -- I got up late.Je me lève avec du retard. -- I get up behind schedule.
The construction Je suis déjà en retard means I am already behind schedule. It is a different construction: être en retard. Here the verb is être. In the example you ask about, the verb is se lever, which requires a slightly different way of phrasing.