It seems that when Lum was born, a postal screwup resulted in a witchy friend of the family not getting an invitation to the celebration. The witch put a curse on Lum, that she would never be happy with her True Love. 

In the present, a new Amusement Park has been built in Tomobiki, and opening day finds the whole gang sampling its pleasures. At a magic show, however, Ataru gets turned into a large pink hippo-potamus, FOR REAL! 

When Lum attempts to track down the magician that transformed her Darling, things start to get very weird, very fast! 

(Source: AniDB)

Strange things begin happening in Tomobiki Town... 

When a great cherry tree, "Tarozakura" is cut down while Lum & Co. are making a movie, Lum loses her horns-and her powers! Thus begins the strangest and most lyrical of the Urusei Yatsura movies...

(Source: AniDB)

The Urusei Yatsura story comes to a climax in this animated retelling of the final Manga story (although not the final movie). Lupa, yet another one of Lum's fiancés, arrives on the scene, and Lum and Ataru have to repeat their game of tag in order to prevent the Earth from being destroyed.

All Ataru has to do to win is say "I love you" the three words he has steadfastly refused to say to Lum. Will he admit his true feelings and save the Earth? Or will his pride doom it to destruction?

(Source: AniDB)

Lupica, another one of the legion of space princesses that all seem to have found out about Earth in some tour book, appears and abducts Ataru! 

But Lupica isn't after Ataru for his great looks or charming personality (because he doesn't have either). Lupica's goal is the greatest love potion in the galaxy, which she intends to use to induce her sweetheart to tie the knot. To get it, she needs the possessor of the greatest lust in the universe...

(Source: AniDB)