I'm going to preface this with the general observation that the sources of occult and conspiracy literature are usually poorly attested, and the writers themselves rarely cite their inspirations, whether or obvious or not. But there's a fairly clear trail on this one, at least at the beginning.

Robert E. Howard's "The Shadow Kingdom" was published in the Aug 1929 of Weird Tales, a pulp magazine of the strange and fantastic. The story involved the resurgence of a population of shape-changing Serpent-Men from prehistoric times, that had survived hidden from humans and seeking to control them. This was a development of a couple themes in Howard's work (serpent worship, Atlantis and an antediluvian age, a hidden race, etc.) which were drawn from a combination of concepts from contemporary anthropology, Theosophy, and popular fiction trends. It's notable that before this, there were basically few if any references to Serpent People or reptilian humanoids in association with Atlantis. Clark Ashton Smith, a friend and fellow-pulpster of Robert E. Howard, paid homage to his story by including serpent people in his story "The Seven Geases" in the Oct 1934 issue of Weird Tales; their friend H. P. Lovecraft made reference to them in several of his stories as well.

In the 1930s, a mimeographed booklet was published titled The Emerald Tablet of Thoth the Atlantean, by Maurice Doreal (sometimes Morris Doreal, real name apparently Claude Diggins), the founder of an occult group known as the Brotherhood of the White Temple. The esoteric poem includes a lot of material drawn from ancient Egyptian religion, Hermetic occultism, and Theosophy, but there's one passage in particular:

In the form of man they amongst us,

but only to sight were they as are men.

Serpent-headed when the glamour was lifted

but appearing to man as men among men.

Crept they into the Councils,

taking forms that were like unto men.

Slaying by their arts

the chiefs of the kingdoms,

taking their form and ruling o’er man.

Only by magic could they be discovered.

Only by sound could their faces be seen.

Sought they from the Kingdom of shadows

to destroy man and rule in his place.

...which is basically a synopsis of Robert E. Howard's Story. Michael Barkun in A Culture of Conspiracy: Apocalyptic Visions in Contemporary America notes that Doreal also authored a pamphlet giving a revisionist history of the world featuring this serpent race ("Mysteries of the Gobi") and another "Flying Saucers: An Occult Viewpoint" (all of these have uncertain publication dates) which postulated this Serpent Race were extraterrestrials.

The early UFO movement of the 1940s and 50s was closely associated with the pulp fiction magazines because of the Shaver Mystery and general similarity of interest, so a pulp influence on an occult writer is not a massive surprise. Reptilian aliens became a feature of science fiction, and were absorbed by degrees into occult and conspiracy literature with works like Robert Ernst Dickhoff's Agharta (1951, serpent men from Venus come to Atlantis and Lemuria) and you can see the sort of divergence that gave us reptilian aliens like the Gorn for Star Trek versus the tabloid fodder that the British Royal family are serpent-people, which makes its appearance in the 1980s.

Doreal would be a source for later works like David Icke's Children of the Matrix: How an Interdimensional Race has Controlled the World for Thousands of Years-and Still Does (2001), which sort of collates and updates the whole idea.