If it comes and goes, then it's not an infection like in her sinuses - that would be constant. I just got over a sinus infection, so the memory is still quite fresh (LOL!) in my mind.
I would say that since it comes and goes it's likely more nerve related. Lyme can destroy the myelin sheath, which is a protective covering that the nerves have. Without this covering, the nerves get and send wonky signals at times, so we have random pains that are not able to be attributed to a specific cause - other than Lyme.
Since it's in her face like that, it sounds like Trigeminal Neuralgia:
patient.info/health/trigeminal-neuralgia-leaflet and we know that it occurs with Lyme:
www.columbia-lyme.org/patients/ld_lyme_symptoms.html