Our sensor can give a very good reading of the earth's field. Yes, electric motors usually generate magnetic fields that will add to the earth's magnetic field. The sensors will detect the sum of these fields as one field. Also, ferrous objects will distort the earth's field causing the strength and direction to change near it. I do not mean a direct strike.
Lightning has no effect on the magnetic properties of the sensor if it struck nearby.
There may be a change on a vehicle if it is struck by lightning, but only a shift. The vehicle would still be detected as it passed by the sensor - it may have a little different shaped response though. The effect of mounting a magnetic sensor on a vehicle will distort the earth's field. This distortion can be calibrated with the simple technique of moving the vehicle around in a circle. There is no limitation to the speed of the vehicle on the magnetic sensor.