You're correct that in the
Dragonsfoot thread Gygax is talking about what he considers to be Lawful Good, indeed, paladin, behaviour within the fictional world of D&D. But he also uses claims about the real world to justify that behaviour.
In the thread, Gygax says there are three different circumstances in which a Lawful Good paladin could kill prisoners:
1) Meting out punishment for a crime. "An eye for an eye and a tooth for a tooth is by no means anything but Lawful and Good."
2) Executing a convert so as to prevent the possibility of backsliding. "A paladin can freely dispatch prisoners of Evil alignment that have surrendered and renounced that alignment in favor of Lawful Good. They are then sent on to their reward before they can backslide."
3) "The old addage about nits making lice applies."
Both (1) and (3) are justified by reference to the real world. In the case of (1) Gygax talks about the brutal "Anglo-Saxon punishment for rape and/or murder of a woman". In support of (3) he provides
the following argument (emphasis mine):
Gygax is making a claim about the real world. He is saying that it is a "fact" that the women and children of ethnic groups considered to be the "enemy" will produce more enemies. This "fact" was used by Colonel Chivington and others to justify genocide.
Historical Background on "Nits Make Lice"
In 1864, Colonel John Chivington presided over a massacre of nearly two hundred Cheyenne and Arapaho "elders, women, warriors, and children" (Kane) at Sand Creek in Colorado. Katie Kane,
Nits Make Lice: Drogheda, Sand Creek, and the Poetics of Colonial Extermination (1999):
In the outcry among citizens of the Eastern part of the United States following the genocide at Sand Creek, a congressional hearing was held to investigate the charges of excessive violence and murder carried out by the Third Cavalry Regiment of Colorado Territory under the order of John Chivington. One congressional witness, S. E. Browne, credited Chivington with uttering the phrase that would resonate throughout the subsequent history of U.S.-Native American relations. Browne recalled the colonel's articulation of his strategy with regard to Colorado's "Indian problem": "early September or late in August last I heard Colonel Chivington in a public speech announce that his policy was to 'kill and scalp all, little and big; that nits made lice.'"
Kay Wright Lewis,
A Curse Upon the Nation (2017), on the term's 17th century origins:
John Nalson, an English clergyman and historian, was told by a captain in the English army that "no manner of Compassion or Discrimination was shewed either to Age or Sex, but that the little Children were promiscuously sufferers with the Gulley [a large knife], and that if any who had some grains of Compassion reprehended the Soldiers for this unchristian inhumanity, they would scoffingly reply, Why? Nits will be Lice, and so would dispatch them." It is at this point that "the saying 'Nits will make lice,' which was constantly employed to justify the murder of Irish children," became part of English vernacular.
He quotes a phrase historically used to justify the slaughter of noncombatant women & children, and references a specific person who used it for that purpose.
