Cessna 172 Flight Instructor reported witnessing student runway excursion and striking runway edge lights during student solo flight.

Narrative

During a supervised student solo flight in a training aircraft; the student landed RWY XX at ZZZ and allowed the aircraft to drift off the paved runway surface at low speed during rollout. I was standing nearby on the ramp with a handheld radio; and heard tower give a wind-check for winds greater than what were forecasted or reported after the student had departed. It is my understanding that the aircraft entered the grass adjacent to the runway and struck a runway edge light as the student was focusing on keeping nose up and wings level during the landing. Student did not lock up the brakes. No injuries occurred and the aircraft sustained no damage. Airport operations responded and confirmed the light was minor airport property damage and a non-issue per maintenance personnel.The event was discussed in extreme detail during post-flight debrief; emphasizing GO-AROUND decision making being paramount -- directional control; crosswind correction; and maintaining runway centerline during rollout. Additional training will be imperative.