Gygax's take on alignment is fascinatingly horrific and was non-viable as of 2E, if not earlier, but it is interesting as it does match one DM I played with, who had started with 1E and played 1E a fair bit (with older 1E players) who had identical attitudes of the "genocide is Lawful Good" type.
In the Dragonsfoot thread, Gygax regards lawful good as very different in its approach to neutral good or chaotic good.
Gary Gygax said:
The non-combatants in a humanoid group might be judged as worthy of death by a LG opponent force and executed or taken as prisoners to be converted to the correct way of thinking and behaving. A NG opponent would likely admonish them to change their ways before freeing them. A CG force might enslave them so as to correct their ways or else do as the NG party did.
Source
Upthread, Gygax says that the second lawful good option "taken as prisoners to be converted" can be followed by immediate execution.
Gary Gygax said:
As I have often noted, 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.
Source
This seems to be inconsistent with the account of good and lawful good alignment in AD&D 1e.
Players Handbook (1978), emphasis mine:
While as strict in their prosecution of law and order, characters of lawful good alignment follow these precepts to improve the common weal. Certain freedoms must, of course, be sacrificed in order to bring order; but truth is of highest value, and life and beauty of great importance. The benefits of this society are to be brought to all.
To a lawful good character, life is of "great importance" and benefits "are to be brought to all."
Dungeon Masters Guide (1979), emphasis mine:
Basically stated, the tenets of good are human rights, or in the case of AD&D, creature rights. Each creature is entitled to life, relative freedom, and the prospect of happiness. Cruelty and suffering are undesirable.
Creatures of lawful good alignment view the cosmos with varying degrees of lawfulness or desire for good. They are convinced that order and law are absolutely necessary to assure good, and that good is best defined as whatever brings the most benefit to the greater number of decent, thinking creatures and the least woe to the rest.
The first paragraph is about all good alignments, the second only refers to lawful good. In the last sentence of the second paragraph there is a suggestion that "creature rights" might not apply to orcs and other humanoids, because they would not be considered "decent".
Gygax has been consistent about the idea of a paladin immediately executing converts. "From the Sorcerer's Scroll",
Dragon Magazine #38 (1980):
A Paladin could well force conversion at swordpoint, and, once acceptance of the true way was expressed, dispatch the new convert on the spot. This assures that the prodigal will not return to the former evil ways, sends the now-saved spirit on to a better place, and incidentally rids the world of a potential troublemaker.
In the same article, he discusses a lawful good ranger protecting a wounded wyvern. Wyverns are of low intelligence, 5-7, in AD&D 1e.
To assert that a man-killing monster with evil tendencies should be protected by a lawful good Ranger is pure insanity. How many lives does this risk immediately? How many victims are condemned to death later? In short, this is not good by any accepted standards! It is much the same as sparing a rabid dog or a rogue elephant or a man-eating tiger.