What does R. A. Lafferty mean by the word "recension"?

The Compact Edition of the Oxford English Dictionary (1971 edition) lists several meanings of recension (presented here without the dictionary's included citations):

1. An enumeration, survey, review. Now rare. (Freq. in 17th c. esp. in Evelyn's works.)

b. A review (of a book). rare^—1

2. The revision of a text, esp. in a careful or critical manner; a particular form or version of a text resulting from such revision.

b. transf. A revised or distinct form of anything.

Definition 2(b)—which is extremely broad—seems to be the sense in which Lafferty uses the word recension. The OED finds instances of the word used in this sense going back to 1835 and 1859, both by the same author, Isaac Taylor. The earliest cited source, Taylor, Spiritual Despotism (1835) actually uses the term twice:

But there is yet an opinion of the Lutheran Reformation entertained by those who, using themselves to institute impartial comparisons of religious systems, decline either to accept, or to reject, any particular recension of Christianity, in mass ; and especially, who anxiously desire to see Christianity freed from the bonds of every peculiar version, and given to mankind in its primitive energy.

...

Unhappily, at present, the prejudice prevails which prevents its being seen that ancient books perhaps intrinsically undeserving of perusal, may nevertheless claim attention, in a peremptory manner, as the sources and materials of history. Uninformed of the history of Christianity, we are the creatures of that recension of Christianity which happens to be current in our times.

Merriam-Webster's Eleventh Collegiate Dictionary (2003) ignores the generalized sense of recension in its entry for the word:

recension n (c. 1828) 1 : a critical revision of a text 2 : a text established by critical revision

But the much larger Webster's Third New International Dictionary (1986) has the following additional relevant definition:

recension n ... 3 : a revised form of something {started a vogue for sophisticated recensions of ancient myths —Paul Pickrel}

From these dictionary treatments and examples, it appears that the generalized sense of recension emerged early in the word's career in English, and that the generalized sense's tie to recension as a term connected to versions and critical revisions of (especially religious) texts remains influential in determining the contexts in which use of the word seems appropriate. Lafferty's use of recension ventures fairly far afield from that connection; but the connection remains visible in some of the instances that the OP presents. Today most writers might be inclined to use a word such as version, iteration, or incarnation in place of recension as used by Lafferty.

Recension (from Online Etymology Dictionary)

The Etymology points toward a meaning of "enumeration" or "versioning". Just as texts are enumerated by revisions, people are enumerated by generations. Beyond that, I can see the meaning being stretched to encompass a group of the same kind or descent such as a clan or family.

They have never intermarried with the children of Adam except once. And not being of the same family they are not under the same curse to work for a living.

They have been separated for many years. The three children were reared by their father under the clan and curse of Adam.

It was named Little Briar-Rose (Dorn-Roschen). Though written more than a hundred years after the Perrault story, Little Briar-Rose is of an earlier Generation.

For objects it implies the existence of different versions.

2004 Times Lit. Suppl. 16 Apr. 20/2 Westwood offers kitsch interpretations of classic British dress, including a range of tartan mini-kilts and several stylish versions of Miss Marple's thornproof Harris tweeds.

Homer had a little trouble with the doorknob. They don't have them in all variants, you know; and he had that off-the-track feeling tonight. But he figured it out (you don't pull it, you turn it), and opened the door.