Final answer:
The inciting incident in 'Lather and Nothing Else' occurs when the barber identifies Captain Torres as his customer, igniting the barber's internal conflict and moral dilemma that comprises the story's central plot.
Step-by-step explanation:
The inciting incident in the short story 'Lather and Nothing Else' is the moment when the barber realizes the man sitting in his chair, whom he must shave, is Captain Torres, a notorious executioner of rebels. This recognition sets into motion the barber's internal conflict of deciding whether to kill Torres to support the rebels' cause or to perform his duty as a barber professionally and not betray his personal ethics. This critical event thrusts the protagonist into a moral dilemma that drives the story forward.