Flight Instructor reported a loss of control by a student during a presolo lesson in which the aircraft veered left off the runway. No injuries or damage reported.

Narrative

Our presolo lesson went well; student was going through checklists and did 5 landings without CFI input. I also prompted a go around and student went through it without issue. The solo lesson started with us reviewing a bit about traffic pattern procedures and mentioning various reasons to initiate go-arounds in the name of safety; and importance of flaring. Weather was good and didn't change much from our dual flight. Winds were especially good as they ranged from calm to just a few knots (under 5 knots). The flight portion started off with the student having trouble starting the airplane. I meet her outside her plane on the ramp and had her go through the flooded engine start checklist. The engine started right up after she went through the normal checklists procedures before taking off. The first landing looked alright and the student taxied back to the start of the runway for the second landing. For the second landing her downwind looked good; base to final looked a bit high and on final she got to the point where she was over the numbers on the runway and still a bit high. From my point of view she pitched down a little aggressively to try to put the plane down faster or perhaps tried to land where we usual had touched down. At first I was watching her and worried that she wouldn't flare enough but she did flare coming over the runway. It seemed like she touched down okay but then suddenly veered off to the left and went off the runway; perhaps resulting from coming in fast. We had talked about a few situations regarding this as far as going around if we are too high and would have to nose down for the runway & making smooth brake/rudder inputs if we're fast to not over control the plane.After witnessing the [incident]; I ran over to our flight school's dispatch desk and had them call line service while I ran to meet the student in the plane. When I got there the engine seemed off but the mixture; throttles; magnetos and fuel selector were still on/forward so I had the student set these items off/idle. After this the student exited the aircraft and we both went inside the FBO to debrief.