Yes, the sentence "My night sleep routine has been messed up lately" is grammatically correct. It means that the speaker's usual routine for sleeping at night has been disrupted or altered recently, which may lead to difficulties in getting a good night's rest.
Here are a few rephrased versions of the sentence:
1. "My nighttime sleep routine has been disrupted lately."
2. "I haven't been able to maintain my usual nighttime sleep schedule