James Churchward did mention the Neanderthal in his books.
From the 1926 Lost Continent of Mu Motherland of Man, he wrote:
In their excitement over the discovery of a few old human bones, such as the Neanderthal, Piltdown, and Heidelberg man, scientists, in both Europe and America, have completely ignored and cast aside the remains of ancient man in North America.
That the European remains were those of idiots and degenerates is obvious from the abnormal shapes of their skulls. Doubtless they were outcasts from civilized communities.
It is geologically admitted, as we have previously pointed out, that the European ape-like beings-the Piltdown man, the Heidelberg man and the Neanderthal man-lived some time during the early Pleistocene, or after the date of Niven’s upper city. Thus Niven’s discoveries emphatically show that man was in America in a highly civilized and cultured state tens of thousands of years before the European ape-like men lived, and proves beyond question that they were individuals and not types.
Certainly he would have scoffed at the recent discovery mentioned under the title, “First Love Child of Human, Neanderthal Found,” which indicates that an individual living 30-40,000 years ago has been identified as a Neanderthal-Human hybrid. They are working on analysis to show that Humans and Neanderthal interbred, since 1-4% of European and Asian DNA is from the Neanderthal. I was a little curious about how the researchers arrived at the conclusion that the human males raped neanderthal females in an early form of ‘ethnic cleansing.’
Other researchers have also proposed that rather than being a separate, distinct species homo sapiens, that we are derived from a number of other hominids, such as the Neanderthal, Denisovan, or Homo floresiensis (the “hobbit”) and maybe more that we have not even discovered yet.
Have a great day.