I'm not sure if the company is a monopoly or oligopoly. There is a patent on the their product which is a characteristic associated with a monopoly but they do have competition which is not a characteristic of a monopoly. The company has very few competitors which makes me think it is an oligopoly but I'm not sure if I'm on the right track.
The question of whether LoJack is a monopoly or not will depend on how you classify the product. They have competition in the sector they operate, vehicle and asset tracking. In fact one company has an image on its website that says NO JACK! But, the number of companies competing against LoJack in the vehicle recovery and tracking system is very small. The only ones I could find in the US are ...
LoJack is a manufacturer of anti-theft devices. This posting looks at the structure of the market in which LoJack operates, and the competition it faces.