For actual FIRE, you need 3 things. Fuel, Oxygen, and Ignition. Ignition could have been caused by an arc. Oxygen is pretty obvious here. What you're lacking is fuel. Plastic (like around the wires) can burn but its ignition temperature is much higher than an arc from anything in that area can create. If somehow there was something in the lighter socket, like lighter fluid, a metal-and-paper bubblegum wrapper (ignition & fuel in 1 package), or something like that, a very short and low-power arc (not enough to trip the fuse) could ignite it and it would burn till the fuel ran out.
Still, that's a series of unlikely events. Unless you were pranked or something.