The primary conflict in Roald Dahl's "The Landlady" is man versus man, specifically between Billy Weaver and the landlady. This conflict is largely psychological, as Billy initially perceives the landlady as a kind, hospitable woman, but gradually becomes aware of the sinister reality behind her seemingly benign exterior. The tension arises from Billy's growing unease as he notices odd details about the landlady and the bed and breakfast, leading to the realization that something is deeply wrong. This conflict is driven by the landlady's deceptive nature and Billy's struggle to understand the danger he is in, creating a suspenseful and unsettling atmosphere.