Kaori Sasaki—a member of Uchihama Academy's Astronomy Club—confesses to Sou Akiyama, but later that evening, she dies in a tragic road accident. Her friends and fellow club members mourn her death in a local hospital. Yet she shows up to school the following day, and no one senses anything amiss. The day finishes without any unusual incidents, and the group of friends plans for the upcoming cultural festival. Suddenly, the room is shaken by an unnatural earthquake. Everyone splits up to investigate—except for Nagisa Hanamiya, who stays behind. As everyone leaves, Nagisa notices that the odd relic-like cube that she was toying with starts emitting a strange blue light. Meanwhile, Sou stumbles upon an unconscious, naked girl lying in a pool of water. Ushinawareta Mirai wo Motomete follows the Astronomy Club's increasingly bizarre adventures—from dealing with ghosts to quelling unrests between student clubs. All the while, they unravel the circumstances behind the sudden appearance of a new transfer student.

Upon regaining her senses, Yui Furukawa discovers that the current day is July 13—a starting point that she has never experienced prior. However, despite the unfamiliar circumstances, she resolves to spend her summer vacation with the other members of the Astronomy Club at Nagisa Hanamiya's family villa. The house and its surrounding area have a rich history; a renowned scientist, Nagisa's great-grandmother researched and developed technology at the nearby military manufacturing plant. While the Astronomy Club is having fun at the beach, a sudden storm stops their plans short. Left with no other choice, the group takes shelter at the abandoned factory, eventually leading them to explore a hidden underground bunker. What they encounter there may reveal an unprecedented connection to a lost future.

When aliens known as the Oni threaten to invade the Earth, they promise to leave under one condition—a randomly-chosen human must win a one-on-one game of tag against Lum, the beautiful daughter of the Oni leader. The lucky person selected happens to be the lustful and unlucky high schooler Ataru Moroboshi. Given 10 days to attempt to grab Lum's horns, Ataru realizes how impossible the challenge is as he is faced with Lum's extraterrestrial powers. Motivated by a promise of marriage from his childhood friend Shinobu Miyake, Ataru manages to catch Lum off guard. He mistakenly grabs hold of her bikini top first, but he eventually achieves his true goal. Although the game is over, Lum misunderstands that she is the one whom Ataru wants to marry, and she decides to move in with him. The poor student constantly tries to shake off the clingy Lum while doing his best to reconcile with his desired fiancée. After Ataru's heroic feat results in such a disastrous outcome, it is questionable whether luck will ever be on his side.

Lum doesn't need much assistance going ballistic when everyone in Tomobiki gets an invitation to Ataru's wedding -- and she's not listed as the bride! It seems that some 11 years ago, Ataru played Shadow Tag with a young girl named Elle and won. Unfortunately, Elle was yet another Alien Princess; and on her planet, if a boy steps on a girl's shadow, they have to marry. When Elle's emissary comes to make arrangements, Lum redefines the term the atmosphere was electric, but to no avail: a force-field now protects Ataru from her high voltage love-zaps. Lum's friend Benten suggests a pre-emptive wedding, and they proceed to abduct Ataru and all of the wedding guests, and the stage is set for the shotgun wedding of all time! (Source: AniDB)