A technician will typically inspect the burner or igniter, flame sensor, blower, filter, and heat exchanger, and test combustion and draft on oil and gas units. On an oil furnace, routine service often includes a new nozzle and fuel filter, so ask what was done.
If replacement comes up, the contractor should explain the permits: the Building Department handles mechanical and gas permits through Viewpoint, while oil burners go through the Fire Department. A paper building permit application in Lakeville must include a copy of the contractor's license and proof of liability and workers' compensation insurance, so ask to see both.
In older Lakeville houses, expect a look at the ductwork as well. Leaky or undersized ducts can make a new furnace seem weak, and sealing them is sometimes part of the right fix.