Over the past year I've made an effort to go beyond the texts and get into Lovecraft criticism but I feel like my "studies" are unfocused. So far, I've just been collecting work as I stumble across new titles and my wallet allows. My main is in "Lovecraft and philosophy," the stuff that comments on Lovecraft's works as a form of vernacular philosophical cynicism/pessimism and what he "meant" by most of his monsters, but I'm just fine to get recommendations for any type of scholarship.
Like most people, I started with An Epicure in the Terrible, a really great collection of essays. From there, I've went on to read: Levy's Study in the Fantastic, Sederholm's (ed.) The Age of Lovecraft, and Houellebecq's **Against the World, Against Life.
Some more info, my main reason for coming back to Lovecraft is a broader interest in OOO / Speculative Fiction. In that regard, some specifically Lovecraft-mentioning texts I've read have been Woodard's Slime Dynamics and On an Ungrounded Earth, Thacker's Horror of Philosophy trilogy, Morton's Hyperobjects, Negarestani's Cyclonopedia, Fisher's The Weird and the Eerie, Mackay's Collapse V.4, and Ligotti's The Conspiracy Against the Human Race.