The main themes of D&D – heroic fantasy, Good vs Evil, zero to hero, flashy magic – are not Lovecraftian. But, to add to what
@pemerton said, there are a number of Lovecraftian elements in the 5e D&D core rules:
The "Great Old One" warlock patron, the Far Realm, Tharizdun, cultists, ghouls, and amorphous tentacled monsters such as the gibbering mouther and yochlol demon. The roper comes directly from the TV show Space: 1999 but I don’t think it could’ve existed without Lovecraft.
The Yuan-ti probably derive partly from the Lovecraft story The Curse of Yig. This curse turns human beings into snakes. Yig is worshipped by Native Americans. The human ancestors of the Yuan-ti "worshiped serpents as totem animals" (5e MM). They live in Mesoamerican-style step pyramids. Robert E Howard’s serpent people and their almost human descendants in The Children of the Night and People of the Dark were likely also a source.
The Points of Light setting somewhat resembles Lovecraft’s cosmic horror but on a smaller scale. Most of the default 5e D&D world is monster-infested wilderness. "Wild regions abound. City-states, confederacies, and kingdoms of various sizes dot the landscape, but beyond their borders the wilds crowd in. People know the area they live in well... but few know what lies beyond the mountains or in the depths of the great forest" (5e DMG).
Likewise in Lovecraft's Mythos stories the distant past, the far future, space, other dimensions, the sea deeps, and parts of rural New England, among other places, are all the realm of monsters. "We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far." (The Call of Cthulhu). In D&D otoh the PCs
are meant to voyage far - that's the game!
5e PHB (emphasis mine):
THE GREAT OLD ONE
Your patron is a mysterious entity whose nature is utterly foreign to the fabric of reality. It might come from the Far Realm, the space beyond reality, or it could be one of the elder gods known only in legends. Its motives are incomprehensible to mortals, and its knowledge so immense and ancient that even the greatest libraries pale in comparison to the vast secrets it holds. The Great Old One might be unaware of your existence or entirely indifferent to you, but the secrets you have learned allow you to draw your magic from it.
Entities of this type include Ghaunadar, called That Which Lurks; Tharizdun, the Chained God; Dendar, the Night Serpent; Zargon, the Returner; Great Cthulhu; and other unfathomable beings.
5e DMG:
THE FAR REALM
The Far Realm is outside the known multiverse. In fact, it might be an entirely separate universe with its own physical and magical laws. Where stray energies from the Far Realm leak onto another plane, matter is warped into alien shapes that defy understandable geometry and biology. Aberrations such as mind flayers and beholders are either from this plane or shaped by its strange influence.
The entities that abide in the Far Realm itself are too alien for a normal mind to accept without strain. Titanic creatures swim through nothingness there, and unspeakable things whisper awful truths to those who dare listen. For mortals, knowledge of the Far Realm is a struggle of the mind to overcome the boundaries of matter, space, and sanity. Some warlocks embrace this struggle by forming pacts with entities there. Anyone who has seen the Far Realm mutters about eyes, tentacles, and horror.
