What is the barber's internal conflict or dilemma in "Just Lather, That's All"?
The barber is faced with both a moral and professional dilemma: He would love nothing better than to cut the throat of Captain Torres, the man who had hunted down and killed and tortured so many of the barber's rebel comrades. Torres's death would bring an end (at least temporarily) to the revolutionaries' greatest threat. But the barber is also faced with his foremost professional ethic: As a barber, his code requires that he never spill a drop of his client's blood, and deliberately killing Torres would breach this code. The barber was also faced with a personal conflict. If he killed the captain, his identity as a rebel would be exposed; additionally, he wondered,
... what would I do with the body? Where would I hide it? I would have to flee, leaving all I have behind, and take refuge far away, far, far away. But they would follow until they found me.
The barber also realized that Torres would simply be replaced, possibly by another man even less civilized than the captain.
Others come along and still others, and the first ones kill the second ones and they the next ones and it goes on like this until everything is a sea of blood.
So, partially out of fear for his own safety; partly out of the realization that he still might be able to better serve the rebel cause by remaining anonymous; and in part because he could not break the barber's code, he decided to simply complete the shave and send the captain on his way.