Clyde is a several-hundred-year-old vampire and currently living in a lemon grove in Sorrento, Italy with his vampire wife Magreb. Cursed with immortality and an unquenchable thirst, the couple searches for ways to pass the time. Clyde spends most of his time sitting in the grove watching lemons fall from the trees and avoiding tourists while his wife sleeps in a nearby bat cave. Because of his old age, Clyde is unable to transform into a bat and cannot join her. No longer as youthful as he once was, Clyde has become something of a grandfather figure to Fila, a worker at the grove who knows he's a vampire and gives him lemons for free. At night, Magreb and Clyde sink their teeth into lemons, which satiate their hunger for a few hours, but are ultimately unsatisfying.
In his younger years, Clyde had been convinced that all the conventional stories about vampires were true. He drank blood, wore a fancy cape, avoided sunlight, etc. When he met Magreb, however, he learned that blood does nothing to quench his thirst and that the myths about vampires were all fictions that he had to overcome. As they traveled the globe searching for rest and respite from their hunger, Clyde began to work through his fears and live a happier life. These travels brought them to the lemon grove.
But despite the lemons, the couple begins to grow restless. They are tired, nowhere closer to being satisfied, and growing apart from each other.
In one last effort to save his marriage, Clyde takes Magreb to a movie, where he sees the young Fila on a date a few rows ahead of them. When the projector malfunctions, the audience spills out into the night. Magreb heads home to the bat cave, and Fila comes to talk to Clyde. The girl playfully lures him into an alley and exposes her neck. Unable to stop himself, Clyde attacks Fila, stealing a key from Fila's pocket but not drinking her blood. The key is to the funicular that carries people up to the bat caves, so Clyde takes one up, even though taking it feels degrading to his kind. he searches in the cave for Magreb. Unable to find her, he descends to the lemon grove alone, hoping she will appear in the morning.