Why is je me levée en retard wrong when je suis déjà en retard is righ?

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.

Hmmm. Not real clear but I sort of get it.  To be late is different then to get up late in French. 

I don't think there's anything wrong with "Je me suis levée en retard". On the other hand, "avec du retard" sounds more like "with a delay", which doesn't seem to fit here.