Lovecraftian in the sense of - they enter the universe from outside it. They are an imposition of existence out of nothingness that was not and now is. I existed for twenty-seven years before my daughter was part of the universe. She will never, truly, comprehend that, because her universe began to exist only when she was born.
Lovecraftian in the sense of - they manifest themselves within the flesh of an adult human and wrench their way bodily into the material plane in a nightmare day-long ritual of pain and gore. Have you even seen afterbirth? Google it. Tadah! Now you know how Shoggoths look. (Or DnD Black Puddings).
Lovecraftian in the sense of - they are (at least to begin with) a profoundly abstract consciousness, a minimal, machinelike, binary dot of need or satiation. They comprehend nothing and experience everything in ways that adults have forgotten.
Lovecraftian in the sense of - they are vampires. Fucking vampires. They feed on your energy and love and use mindrays (and oxytocin) to enslave you. I am a ghoul now. I am a sleepless thing eating bugs and worms. I exist to serve the beast.
Lovecraftian in the sense of - they are a physical manifestation of deep time, and the knowledge you will be superceded and forgotten, and only through mimicry and memetic transfer can you hope to raise feeble dams against the onslaught of entropy that will drown the fortresses of man.