What is the purpose of this current sense resistor in my arc lighter?
I have seen a similar circuit used in my Gas operated water heater it also consist of an electric arc generating circuit and operates on two D type cell battery.
And have tested that circuit and I got to know that this kind of circuit need to change the Ton Time of the MOSFET to generate proper electric arc between their electrodes as fix duty cycle will not work efficiently in such case, as battery voltage will be gradually reduced Ton time should be increased.
So as I think in your case R12 provides a low resistive path for most of the current to flow to the ground and with a high resistor value like 4.7k R11 is used to sense voltage feedback so that it can vary the duty cycle accordingly.
Still, I am not 100% sure about this but you can test it with an oscilloscope and providing a variable power supply to the circuit.