So, I've been trying for a long time to find an answer to the two questions:
Did the Inklings ever read Lovecraft?
Did Lovecraft ever read the Inklings?
So far as the first question goes, the answer is: still not proven. We know that Warnie Lewis was a fan of 'scientifiction and read some of the pulp magazines like AMAZING STORIES. And THE NOTION CLUB PAPERS suggests that the Inklings were fairly conversant in science fiction. Certainly there are some echoes of Lovecraftian themes in Tolkien's account of the Things beneath Moria, Lewis's description of the subterranean world far beneath the surface of Venus, and especially Wms' Cthulhesque octopoid-lords of P'o-l'u. Williams was well-versed in fiction dealing with occult themes and was well-positioned to have come across at least some mention of HPL. But resemblance is not proof and the question remains open.
The second question seemed much more unlikely: Lovecraft died too soon, the same year THE HOBBIT came out and a year before OUT OF THE SILENT PLANET, neither of which is much like the kind of books Lovecraft read.
Despite this, the answer turns out to be YES: towards the end of his life Lovecraft read four of Wms' five novels (the sixth and seventh having been published in 1937 and 1945 respectively).
The proof comes in DAWNWARD SPIRE, LONELY HILL (2017), the collected correspondence of H. P. Lovecraft & Clark Ashton Smith. I was looking through this for something else entirely, evidence of when HPL and CAS first read the work of Wm. Hope Hodgson, to find that the same person who brought the long dead and wholly forgotten Hodgson to Lovecraft's attention also loaned him two novels by Charles Williams (p.566), who in turn passed them on to Smith (.572, 574).
Of these, Lovecraft preferred WAR IN HEAVEN (.575), Wms' grail novel and my own personal vote for his best book. The editors of the correspondence, Schultz & Joshi, speculate as to which of Wms' novels the other book cd be (.575 Note 4), but actually no speculation is needed, since Lovecraft ends his previous letter "Yrs for the Stone of Suleiman" (.574). Lovecraft had the habit of opening and closing his letters with cryptic, evocative phrases: the letter before had ended "Yrs. for the sunken monolith of Gnoph" (.573); a subsequent letter describing his reaction to THE NIGHT LAND ends "Yrs for The Watcher of The Northwest" (.587), a clear reference to one of the sinister Great Old Ones -like figures that feature so prominently in Hodgson's book. And since The Stone of Suleiman is the key magic item around which MANY DIMENSIONS, William's sequel to WAR IN HEAVEN, centers, it seems certain that this was the other book Lovecraft and Smith read in the fall of 1934.
Schultz & Joshi note that C. L. Moore, one of the HPL's disciples, sent him two more Charles Williams books in February 1936: THE GREATER TRUMPS (his tarot novel) and THE PLACE OF THE LION (the danger of Platonic ideals; .575nt4). The one Wms novel Lovecraft didn't read in 1934 and 1936 was thus SHADOWS OF ECSTACY (his worst novel). CW's final two novels, DESCENT INTO HELL (1937) and ALL HALLOW'S EVE (1945), having been published too late for Lovecraft to have had time to read them.
So the answer is: yes. As for what Lovecraft thought of Wms, I'll save that for the next post.