From "The Effigy Histories:"
"...for he had the various shapes and attitudes of a person who knows everything. Those shapes and attitudes are intuitive, and they are always to be recognized. And they cannot be faked.
And Karl Effigy did not know everything, because all his pleasant Histories were nonsense, and so were his pleasant explanations of them."
From "The Casey Machine"
""In times before this, several other organizations of illuminated persons have known everything. They knew everything, before their own deaths, by making a Particular Judgment in their own lives. But we become masters of our own judgment in a way the earlier ones could not, because we live in an age of electronic amplification and switching and data control. We are able to project it all, and to repeat it. Yes, and we are able to sell it."
Besides “The Men Who Knew Everything," there are others in Lafferty's fictions who knew everything. Diogenes Pontifex, that elegant man not quite of the Institute, is said to have been a man who knew everything. The other elegantly indecent non-member of the Institute, Audifax O’Hanlon, is described as “quite ordinary except for one double-edged gift: he knew everything that had been, and everything that would be.”
Oread Funnyfingers went to school only for seemliness. She already knew everything. Charley Longbank, friend of collector Leo Nation, is also offhandedly described as one who knew everything.
(See “Hole on the Corner,” Arrive at Easterwine, “Funnyfingers,” “All Pieces of the River Shore.”)
In Reefs of Earth, we read: “As a high master of the Bagarthatch, John Pandemonium was supposed to be a pangnostic, one who knew everything.”
In Archipelago, we are introduced to the Dirty Five “as mythology knows them.” We are told that, “Between them they knew everything, had thought all thoughts, had done all things, or at least had them in mind to do.”
Melchisedech Duffey “knew everything, of course, but that was no special achievement. A lot of them knew everything.”
Hans, one of the Five, “knew everything before everyone else.” Hans also studied under Professor Kirol von Weinsberg, “the last man who knew everything.”
“There can never be another one, as knowledge has so constantly multiplied that it is no longer possible for one man to know it all. It is necessary that there be a new sort of man who is satisfied with only knowing a part of it. It is necessary, but the Professor wouldn't be so satisfied, and neither would Hans.”
In The Devil is Dead, “Papa Devil knew everything.”
There are probably others that I've missed and many further connections to be made.
And as is evidenced in "The Effigy Histories" and "The Casey Machine" (part of More than Melchisedech, the whole of which I haven't tackled yet) excerpts above, there are artificial (and vile) ways of knowing everything and/or ways to know everything but also have it all completely wrong.