When the editor of Whispers in Darkness put out the call for Lovecraftian erotica, I will admit I was as skeptical as other people were. How could an author whose predominant themes were fear and disgust be adapted to the erotic, except perhaps on the superficial level of Japanese tentacle porn?
"Even in the light of his torch he could not help suspecting a slight, furtive trembling on the part of the canvas partition screening off the terrible “Adults only” alcove. He knew what lay beyond, and shivered." -- "The Horror in the Museum"
HP Lovecraft erotica? Tricky. His stories aren't primarily about relationships, but the subjective experience of encountering the unknown. This encounter is generally abortive and unresolved.
There's also the fact that there are hardly any women in Lovecraft's canon. As far as I know, the most prominent women in Lovecraft are Keziah Mason, a child-sacrificing witch with a rat-human hybrid familiar in "Dreams in the Witch House", and Asenath Waite in "The Thing on the Doorstep." Waite's female body is actually inhabited by her father's soul, and her statements about her brain being "not fully human" hint at an unpleasant misogyny.
A lot of Lovecraft stories feature a male-male dyad, consisting of a passive narrator of the story and a more aggressive and domineering man who pushes into the unknown. However, these relationships are only vaguely sketched and don't provide a lot of inspiration for eroticism. (I'm surprised that none of the stories in Whispers feature this kind of homosocial male pair, though "The Artist's Retreat" includes a similar female-female pair.)
Where Lovecraft even implies sex, it's usually in reference to miscegenation, an endemic cultural anxiety of 20th century America. (See "The Shadow over Innsmouth" and "Facts Concerning the Late Arthur Jermyn and His Family") Other authors of the late 19th and early 20th centuries wrote colonialist fantasies of white men meeting exotic beauties; Lovecraft said, "No, you are the product of your great grandfather fucking an ape in Africa."
"Wearied with the commonplaces of a prosaic world, where even the joys of romance and adventure soon grow stale, St. John and I had followed enthusiastically every aesthetic and intellectual movement which promised respite from our devastating ennui. The enigmas of the Symbolists and the ecstasies of the pre-Raphaelites all were ours in their time, but each new mood was drained too soon of its diverting novelty and appeal. Only the sombre philosophy of the Decadents could hold us, and this we found potent only by increasing gradually the depth and diabolism of our penetrations. Baudelaire and Huysmans were soon exhausted of thrills, till finally there remained for us only the more direct stimuli of unnatural personal experiences and adventures." - "The Hound"
However, if you look at Lovecraft in the context of his age, you'll see that it really only requires a slight shift in optic to see the erotic possibilities. Lovecraft's protagonists, even as they are horrified by what they have encountered, are at the same time drawn to it, their own curiosity raised to the level of fascination.
I knew a woman once who was repulsed by the idea of vomit, moreso than most people. However, after I casually mentioned that vomit was one of the more obscure fetishes, she became oddly fascinated by the idea, and when we were planning to go to a BDSM play party, she kept asking for assurances, over and over, that there wouldn't be anybody. It was the repeated questions about this rare kink that made me think she was a little obsessed.
The issue here is knowledge, and there is a long history of the relationship between sexuality and knowledge, going back to Genesis in the Bible. The quest for knowledge, particularly the kind of direct personal experience, easily maps onto the quest for sexual experience. The pre-Raphaelites and Decadents mentioned in the quote above were sexual radicals too, experimenting with homosexuality, fetishism and sadomasochism. Read between the lines of "The Hound" and you'll easily see necrophilia.
"... it proved to be nothing less rare than Pigafetta’s account of the Congo region, written in Latin from the notes of the sailor Lopez and printed at Frankfort in 1598. I had often heard of this work, with its curious illustrations by the brothers De Bry, hence for a moment forgot my uneasiness in my desire to turn the pages before me. The engravings were indeed interesting, drawn wholly from imagination and careless descriptions, and represented negroes with white skins and Caucasian features; nor would I soon have closed the book had not an exceedingly trivial circumstance upset my tired nerves and revived my sensation of disquiet. What annoyed me was merely the persistent way in which the volume tended to fall open of itself at Plate XII, which represented in gruesome detail a butcher’s shop of the cannibal Anziques. I experienced some shame at my susceptibility to so slight a thing, but the drawing nevertheless disturbed me, especially in connexion with some adjacent passages descriptive of Anzique gastronomy." - "The Picture in the House"
Walter Kendrick's history of pornography, The Secret Museum, lays out a theory that began with European scientists excavating archaeological sites like Pompeii and studying "primitive" cultures and analyzing sexual practices. The prevalence of sexual imagery in Pompeii and the variety of sexual customs conflicted with Victorian ideals of modesty and restraint, and the scientists and educators feared that this knowledge could corrupt the "vulnerable persons" (i.e. women, children and the working class). This created the system of classifying knowledge: who could be allowed to know what. Unversities built special cabinets and private collections, restricted to people with the proper credentials. Academic books on sexology like Krafft-Ebing's Psychopathia Sexualis or the works of Havelock Ellis were translated into Latin or kept suppressed entirely to ensure they stayed in the right hands. (To little avail, in the long run.)
You couldn't just walk into a store and buy a copy of de Sade's 120 Days of Sodom or Burton's Arabian Nights or Kama Sutra. You had to know a guy who knew a guy, and just to lay hands on such a book, to possess such rare sexual knowledge was an initiatory, transformative experience. Lovecraft's library of fictional, sanity-altering books comes from the same ideas. He was writing at the tail end of that historical period when knowledge could be kept hoarded by an elite of white, upper-middle class men, before mass literacy and cheap printing made that kind of control impossible. Nowadays, if the Neconomicon did exist, it would probably have been scanned and circulated all over the Internet.
"I shall plan my cousin’s escape from that Canton madhouse, and together we shall go to marvel-shadowed Innsmouth. We shall swim out to that brooding reef in the sea and dive down through black abysses to Cyclopean and many-columned Y’ha-nthlei, and in that lair of the Deep Ones we shall dwell amidst wonder and glory for ever." - "The Shadow over Innsmouth"
The flip side of Lovecraft's alienation, paranoia and xenophobia is a kind of transcendental mysticism, that comes out in his Dreamlands stories but slips into even his most horrific tales. Even as the Lovecraftian protagonists is horrified, he keeps looking, fascinated, even seduced. What is "The Whisperer in Darkness" but a kind of seduction? Usually he refuses the final knowledge, by active resistance, or by passively fainting, but sometimes he accepts and goes over. He transcends his fear and experiences the larger world in a different way, finding beauty where once he only perceived ugliness. As we grow in knowledge throughout our lives, our judgement of that knowledge changes, moving from the instinctive disgust of the different to acceptance and understanding.
"My pets are not pretty, for they come out of places where aesthetic standards are—very different." - "From Beyond"
Thus, Lovecraftian erotica is the encounter with the alien, the transition from horror to ecstacy.