Delay ERROR - RC Circuit
You have a reference voltage of 0.756V on the inverting input (derived from 5V) and therefore you should expect the circuit to "trip" when there is 0.756V on the inverting input. This is equivalent to a current of 0.756 amps through the 1 ohm resistor (R5). So, in fact, you can expect a current equal to or greater than this to eventually cause the comparator to trip.

Is this what you are wanting to happen?

Anyway, inrush current due to the lamp having a lower cold resistance can certainly make the circuit trip sooner. Other problems may be around the comparator - you haven't specified it but input offset voltages and bias currents can all make small errors but, is the comparator capable of working with the signals shown - this depends on how power is connected to the supply pins.