All 7 elements are not required for a story to be Lovecraftian, but a story should have several elements listed below. This is based entirely out of my opinion and is based out of my readings of and reviews of Lovecraft and Lovecraftian literature, as well as referencing movies that are complimentary to the mythos.
1. The Nameless Horror
There is a monster, a creature, something that is actively malevolent, and that creature remains very mysterious, and perhaps exists entirely out of sight, is seldom seen. This is part of the narration, the reader knows nothing more about the foe faced by the protagonists. In the original Alien movie, the titular alien was nameless. The malevolent sentience behind the evil in Event Horizon isn't characterized or personified, but it's just there. Likewise for the demons and monsters from In the Mouth of Madness.
By giving known dimensions to a monster, alien god, or creature is to lessen it's horrific value. The unknown feeds into our primal fear, and where there is a question mark, we are willing to plug in the horrible details from our own imaginations. This is the lingerie for horror, it tantalizes not by what it shows, but by what it doesn't.
2. Queer Folk
When politics and religion, and the more prominent features of our cultures are put aside, people are people and that provides a means of connecting to people across said cultural and ethnic gaps. Queer folk break this connection, they are very different. The Queer folk have something that separates them from the common folk. Like the Innsmouth folk there is just something about them. Sometimes this is really obvious such as the mutations inflicted by radiation, or subtle as the quiet unease in the living room of the suburbanite cannibal household.
The function of the queer folk are to leave the protagonists isolated. They aren't locals, they are tolerated, for now, but they aren't welcome. Sometimes the thing that makes the folk queer is the...
3. Sinister Secrets and Societies
Secrets and secret societies are hallmarks of lovecraftian fiction. There are secret societies that dabble in black magic, or harbingers of a terrible legacy, or a hideous secret. Often the corporation, or the government, or a behind the scenes backer knows what is really going on, and it isn't realized until the end.
One of the most powerful basic plots is Nothing was As it Seemed, and sinister secrets and secret societies are a magnificent, effective, and entertaining way to creating this core plot.
4. Odd Occurrences
There is nothing quite like an odd occurrence to kick off a lovecraftian adventure. A strange object falls from the sky, a research station mysteriously goes silent after a cryptic message, a long missing ship reappears in a strange location.
This can be used as a common trope for starting an adventure, the odd occurrence isn't a McGuffin. It is often the cause and often the catalyst of the entire story, such as the melting meteorite of the Colour out of Space or the books of Sutter Cane (In the Mouth of Madness). A series of odd occurrences can also be strung together to create a map back to the source, unraveling sanity as the events unfold.
5. Strange Places
A proper lovecraftian tale takes place in a strange place. Either the location itself is exotic, such as a lush jungle, a harsh desert plain under an alien star, or the ice scourged wasteland of Antarctica, or something about the location has become strange. There is a strange mist that has isolated the area, or the location has suddenly become otherwise compromised, albeit by a largely unknown power/reason.
The importance of the Strange Place is to remove any aspect of familiar territory from the protagonists. They are in a hostile environment, such as the antarctic, or a disorienting or otherwise challenging location, such as bug filled alien fogs, or a place where their understanding of what is is challenged such as a hotel surrounded by demons that for some reason can't get in. At almost no point should the location be forgiving, or offer anything other than the most cursory respite.
6. Alien Artefacts
Not necessarily being from another world, the alien artefact is something that simply doesn't belong where it has shown up. Alien artefacts lace into odd occurrences, or prompt the appearance of the nameless horror. Artefacts can range from massive objects like mammoth space ships, or cyclopean ruins, to much smaller such as aged carven idols, books written in long dead languages, to things that are simply not describable.
The Artefact creates a focal point in a story, and can be a location (stonehenge) that provides respite, or is the object of the story because finding the artefact is tantamount to ending the horrific events that have started around it, or because of it.
7. Total Party Kill
The final note for the Lovecraftian tale is that the happiest ending allowed is the bitterly pyrrhic victory. In proper lovecraftian horror, the body count is high, and those who manage to survive have their sanity left in tatters, or their soul reduced to shreds. Defeating the alien costs the entire crew, and the ship, except for one escape pod and one (infected) survivor. Even in the best scenario, the protagonists are left with nothing but their lives, any evidence of the event and sacrifices made to stop it are simply gone. In more mainline stories, the monsters laugh and win.
The TPK ending is required for a Lovecrafian story because in the mythos, there is no Happily Ever After for humanity. There is only getting to survive a little longer.