Ransom himself is explicitly based on J. R. R. Tolkien — he teaches the same subject at Cambridge that Tolkien taught at Oxford. (Although in the third book, he seems more like Charles Williams). Tolkien was on the record as saying that he didn't think it was a very close resemblance, although he did recognize some of his own ideas "Lewisified" in Ransom.
Horace Jules, the nominal director of NICE in That Hideous Strength, is a venomous caricature of H.G. Wells.
MacPhee, an Ulster rationalist and Sarcastic Devotee from That Hideous Strength, may have been a fictionalized version of Lewis' old tutor William Kirkpatrick. Or possibly an Author Avatar of Lewis himself, from his days as a skeptic.
Word of God is that MacPhee is pretty much Kirkpatrick; right down to his phrasing.
Defictionalization: In keeping with the new British tendency to de-fictionalize literature critical of the local government (i.e. 1984), there now really IS a N.I.C.E., and the cynical see it heading in the Police State direction. (Though in Real Life it stands for the National Institute of Clinical Excellence and its evil activities are largely confined to denying lifesaving drugs to the sick on the grounds that they would cost the government too much.)
The stated goals of the Voluntary Human Extinction Movement are starting to sound quite a bit like the secret goals of N.I.C.E.
Science Marches On: The canals on Malacandra. Science had already questioned the existence of canals on Mars and Lewis was aware of this, but included the canals anyway.
Also the oceans of Perelandra, back before it was learned that the surface of Venus was a volcanic wasteland hot enough to melt lead.
Shout-Out: The Middle-Earth mythology is referenced in That Hideous Strength—it's implied that King Arthur is of the line of "Numinor" (this was dozens of years before any of Tolkien's Middle-Earth material was published, so Lewis had never seen the proper spelling of "Numenor" by this point).
H.G. Wells. Lewis was very much a fan of Wells' earlier fiction (he used the opening pages of the first book to essentially say that anyone who refuses to read War of the Worlds or The First Men in the Moon is being a snob), but was quite critical of the much more political and less well-remembered utopian novels Wells wrote later in life. (Elsewhere, Lewis compared Wells to Esau, saying that while Esau had sold his birthright for a mess of pottage, Wells had hocked his talent for a pot of message.) Hence, Horace Jules, the clueless pompous twit who is the figurehead Director of the NICE, looks and talks like a Wells parody.
J.B.S. Haldane, with whom Lewis carried on an open debate, is also targeted. Some of Weston's philosophy is almost word-for-word quotes of statements by Haldane. Haldane, in turn, wrote a rather scathing criticism of The Space Trilogy (which Lewis rebutted in the posthumously published essay "A Reply to Professor Haldane").