In my analysis of a particular arc of URUSEI YATSURA stories, I observed that despite the great creativity of manga-creator Rumiko Takahashi, she often didn't go much further than create wacky comic situations.
However, in subsequent stories Takahashi doesn't truly examine the Lum-Ataru relationship in mythic depth. It becomes just a comic routine; Ataru refuses to acknowledge his "marriage" to Lum (or for that matter, whatever genuine feelings he eventually has for her), runs around futilely trying to date other women, and gets punished for it by Lum's demonic powers.Still, like most manga-makers, at some point Takahashi decided to wrap the series, which obligated her to give her readers a finale. However, though the author had suggested the possibility of the two hyper-aggressives being permanently married, she chose not to have them wed at the feature's conclusion. It may be that she wanted to keep the situation open-ended for the purpose of independent anime productions (though only one such production came out in 1991, following the anime-adaptation of BOY MEETS GIRL).
In any case, BOY starts out typically enough. Lum has a minatory dream of impending darkness, but Ataru won't listen as he goes girl-chasing, resulting in the usual chaos.
However, Lum's dreams anticipate a long-buried family secret: that her great-great-great grandfather promised her hand in marriage to a scion of the "World of Darkness." This is a sunless world inhabited by dark-skinned humanoids in Arab-looking attire. The Darkworlders are sustained by mushroom, given that fungi don't need sunlight to grow. Lum's intended, Prince Rupa, shows up on Earth, driving a flying chariot pulled by flying pigs (apparently a reference to porkers and their love of truffles), and asserts that he is to be married to Lum. He slips a ring on her finger, but not just as a promise of his intentions.
Rupa's ring is designed to accelerate Lum's aging process just enough that she loses her horns and her powers, making it easy to do a Hades-routine with Lum as Persephone.
Ataru, belying his usual indifference to Lum, organizes a pursuit party made up of Lum's circle of friends, but as soon as they arrive in the Darkworld, their spaceship crashes into another one. The friends are all captured except for Ataru, who encounters a Darkworld native, Lady Carla, who was the pilot of the other spaceship. She finds Araru and wants him to marry her-- or, rather, to fake a marriage so that Carla can prevent Lum from marrying Rupa, who was at one point Carla's intended.
Without going into all of Takahashi's fine points of comic confusion, Lum doesn't marry Rupa-- not least because she gets back her powers-- but both she and Ataru become estranged, having respectively been convinced that the other has cheated with one of the Darkworlders. Takahashi gives the quarrel an epic connotation, however, in that Lum has finally had enough of Ataru's constant attempts to woo other women. Rupa and Carla are perhaps more substantive threats because they are loose mirror-images of Ataru and Lum, though Rupa is not as lustful as Ataru and Carla is more casually violent than Lum. Rupa returns to Earth with Ataru and the other rescuers, while Lum remains in the Darkworld with Rupa.
Through more comic complications, the Earth gets overrun by Carla's giant mushrooms.
This gives Lum an inspiration. Though she's pursued her "darling" for years, it's always been out of an instinct that he loved her, rather than any outright confession on his part. So Lum makes a deal with Rupa. The two of them will send Rupa's mushroom-eating pigs to devour the offending fungi, if Ataru can win a race against Lum, essentially a replay of the contest that brought them together in the first URUSEI episode, A GOOD CATCH. Lum stipulates that he can only win one of two ways, by grabbing her horns against her will, or by capitulating by admitting his true love for her. (This would seem to be Lum's way of forcing Ataru to make a commitment less equivocal than his apparent marriage-proposal in CATCH.)
Araru defies Lum, believing that he can catch her as he did before, though on another level, he doesn't want her to hear a confession that's been coerced.
To up the stakes even more, Lum unleashes an "amnesia device" that will, if Ataru loses the contest, erase the memories of all Earth-people about their alien visitors. Lum's mix of alien and human friends don't want to forget one another, and try, with slapstick results, to stop the device. As for Ataru, he's determined not to forget Lum, even though he has no chance to capture her against her will.
Takahashi does formulate a way to give Lum her victory without forcing Ataru to make a direct commitment, which, as I said before, allows the author to restore the status quo. Yet on the final page, Takahashi gives her final comment on the "war between men and women." Lum pledges to spend the rest of her life trying to make Ataru confess his love, and he answers that "I'll say it on my death-bed." It's a conclusion that allows Ataru to hold onto his stubborn masculine reticence, and yet also gives Lum a confession more implicit than explicit, thus binding them not to a marriage contract, such as the one Lum's relative negotiated, but a social contract appropriate to their equally bull-headed natures.