Did the two groups read or were they influenced by each other?
Answer: Lovecraft read two of Williams' novels, Tolkien read one short story by Smith, Lewis may have been influenced by a Wandrei tale. Nelson also suggests that OUT OF THE SILENT PLANET was influenced to some degree by AT THE MOUNTAINS OF MADNESS (this seems tenuous) and that the psychic transfer in THE DARK TOWER may owe something to "THE SHADOW OUT OF TIME" (an intriguing suggestion). I found the latter idea the most interesting part of Nelson's paper. Also noteworthy, but less developed, is his idea that there are affinities between "SHADOW OUT OF TIME" and THE NOTION CLUB PAPERS.
Did they admire or were influenced by the same authors (e.g. Blackwood)?
Answer: to some extent, yes. In addition to Blackwood, whom he judges by far the most important shared influence, Nelson considers Dunsany (whom he--quite unfairly I think--calls "the anti-Tolkien"), Hodgson, M. R. James, Machen, and Haggard. He mentions Poe on the one hand and Morris and MacDonald on the other but only in passing: I shd have thought it beyond dispute that Poe was the seminal author for Lovecraft's group; if the Inklings had anyone comparable it wd be Morris and MacDonald.
Is Lovecraft, at his best, 'mythopoeic' as Lewis defined the term?
Answer: that depends. Nelson compares Lovecraft with MacDonald, Haggard, and Lindsay, concluding that these lesser lights, not the Inklings, were Lovecraft's peers. He briefly considers Robert Howard and Clark Ashton Smith, both of whom he considers inferior to Lovecraft: Howard "wallows in violence and sexual perversity" while Smith he finds "misanthropic and decadent", his work marked by "nastiness".
This is a long and discursive piece, its middle section dominated by two and a half pages in small type of extended quotation from THE DUNWICH HORROR and THAT HIDEOUS STRENGTH.** The digression on Bombadil is one of the better things I've seen on that much-misunderstood figure. I do have to say I thought it surprising that when the author criticizes Lovecraft's prose it's not for his idiosyncratic (eldritch!) vocabulary but his use of demonstrative pronoun ("a certain overuse of that and those): odd choice.
I remember someone at Kalamazoo about eight years ago mooted putting together a collection of papers for a book on TOLKIEN AND LOVECRAFT: Nelson's piece wd have fitted well into such a setting. Unfortunately so far as I know that project never got as far as a Call for Papers. Pity, since I knew exactly what I'd like to have submitted: I 'd have loved to have done a short piece exploring whether there was any plausible connection between the Things Gandalf finds below Moria and the creatures Ransom encounters beneath Perelandra and the things that haunt various dark lairs in certain of Lovecraft's Mythos stories. Which wd be interesting to do, but wd take a lot of work, while there are so many other interesting projects in various stages of completion to see to first.
All in all, Nelson's essay is an ambitious piece: worth reading, but might have been better expanded into a short book. There's just too much here to cover in a single essay.
current reading: TRILOBITE!: EYEWITNESS TO EVOLUTION by Richard Fortey (2000; bought 2005, begun and abandoned 2010)
*It came with a TSA tag in it. I now realize it'd gotten misplaced because it arrived right before I went on a research trip and I took it along, thinking I might be able to read it during my down times in the evening. That didn't turn out to be the case, and it came back unread in the middle of a folder of photocopies and miscellaneous notes, said folder having been unearthed in a big re-arranging of my office recently.
**a single paragraph from each wd have served him better.