The patient lay in bed, [waiting for the doctor to come over].
Yes: the bracketed element is a present participial clause functioning as a modifier in clause structure. More specifically, it's a depictive adjunct giving descriptive information about the patient. The actions of laying in bed and waiting for the doctor are contemporaneous.
Note that it is interpreted with progressive aspectuality: The patient was waiting for the doctor to come over.
The patient lay in bed, [waiting for the doctor to come over].
Yes: the bracketed element is a present participial clause functioning as a modifier in clause structure. It's functioning as a depictive adjunct giving descriptive information about the patient. The actions of laying in bed and waiting for the doctor are contemporaneous.
Note that it is interpreted with progressive aspectuality: The patient was waiting for the doctor to come over.