Northern Illinois University has a Lovecraft collection, including letters? Yup

“The collection consists of Lovecraft’s fiction writing, letters, poems, scientific articles, pulp magazine stories, books about Lovecraft, collections of Lovecraft stories, titles of books known to have lived in Lovecraft’s personal library, and a few miscellaneous items, including several manuscript letters.”

No online finding aid to exactly what the collection holds, it seems. Fandom Directory, 2000, confirms there are only “a few letters”.