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.
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