Lovecraft is not required reading for D&D. You might better understand many references within D&D better after having read him, but he's not required by any measure. He's been influential in many key places throughout D&D repeatedly. More recent material has given him more transparent weight, as it were. The appearance of a 'moon calf' in a D&D 3.0 Core adventure path module, for example, or the appearance of the Hounds of Tindalos as a monster in a Pathfinder module.
Lovecraft was never "extremely popular" and still is not. He is, however, popular amongst gamers and SF/F/Horror fans and has ideas were and are extremely influential. But Lovecraft is doesn't rank anywhere on the scale of the recognition of someone like Howard, let alone someone like Dan Brown or Stephen King. He just happens to have been very influential on people who DO enjoy extreme popularity, like Hitchcock, Stephen King and others.