A Flight Instructor reported the student took evasive action during landing roll to avoid a lawn mowing vehicle on the runway.

Narrative

I was involved in a runway incursion and near collision with a farm tractor towing a farm implement yesterday at an uncontrolled airport; ZZZ. This was a part 91 training flight. I was the flight instructor providing upgrade training to the new owner of a new aircraft. We were building proficiency in takeoff and landing operations. The winds were light; it was daytime and the runway was dry. We chose Runway XX to take advantage of the length of the runway; REILs and the two light PAPI on the left side of the runway. We did observe several agricultural vehicles working in and around the airport area apparently cutting hay. My student made standard traffic pattern radio calls throughout the full pattern and had all the exterior aircraft lights on including the strobes and landing lights. My student touched down approximately 500 feet down the runway and on center line. We had planned to let the aircraft roll to the next to last taxiway on Runway XX and we were decelerating normally. As we approached the intersection of Runways XX/XY and XZ/XA; a farm tractor pulled onto the runway and turned east nearly blocking the entire right side of the runway. A go-around was impossible at this point and my student applied heavy braking and nose wheel steering to pass to the left of the tractor. Much of the aircraft's left wing was over the runway lights although none were hit. I spoke with the driver of the tractor shortly after the event. The driver was not sure how she had gotten on the runway; did not hear any of our radio calls (had no radio to monitor) and did not see us as she was not looking for aircraft as she didn't know she had actually driven onto a runway. The tractor was not equipped with any sort of flashing or rotating warning lights. Neither the tractor nor the aircraft were damaged during the incident