I'm wondering if the problem is not in fact related to the lucid dreaming. It sounds like she may simply suffer from insomnia. Plenty of people have regular lucid dreams and do not suffer from it. Lots of people suffer from insomnia however so it may pay to look into solutions for insomnia eg - is the room dark enough? temperature comfortable? good airflow? comfortable bed? no caffeine after 4pm, winding down before bedtime with a relaxing book or meditation, etc etc I suggest you google it.

Another thought... If she is waking up feeling tired and unrefreshed she possibly may suffer from sleep apnoea.