The answer to your question is in the word 'lather'. it has 2 meanings. one which refers to the actual substance applied to an individual's face before a shave and the other which refers to the sweating of a horse due to agitation. The second meanign makes a lot of sense when applied to the Barber because he is very agitated when Torres walks in the shop and The Barber is forced to give him a shave. As well as his constant back and forth about which role will he chose to be in the end; a barber or a revolutionist? In the end, he chose the role of a barber but that's besides the point. The fact of the matter is that the meaning of the title refers to the barber purely being irritated due to the appearance of Torres and nothing more (that's all). The Barber will not go to the extent of attacking or killing Torres and will settle only with his agitation. No more.
There you go... as for the comment before mine, you went straight for the obvious... something a true analyzer would never do.
Shaving with a long open razor blade is a highly skilled job requiring intense concentration:"taking pains to see that no single pore emitted a drop of blood." After lathering his customer's beard with soap, the barber begins to shave the beard with the sharpened razor. As the soap lather and the shaven hair collect on the long razor blade the barber will often pause and remove the lather by stroking the razor on his own bare forearm and will continue shaving. If he pauses every now and then to wash the razor he will take a longer time and more importantly he will lose his concentration.
Although, the narrator-barber is "secretly a rebel, he was also a conscientious barber, proud of the preciseness of his profession." So, the dilemma he faces now is whether to slit Captain Torres' throat or to give him a clean shave without nicking his skin. After quite a struggle within his mind he decides :"I don't want blood on my hands. Just lather that's all."
He puns on the word "blood" to ironically emphasise the fact that "he is a good barber. The best in town." Blood could either mean the blood when he nicks Torres's skin and collects it alongwith the lather on his forearm in which case he would not be regarded as an expert barber or the blood if he murders Torres by slitting his neck, in which case he would be branded a murderer.
The narrator is keen to be known only as an expert barber-only lather on his hands.