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)

AD 3567. Mankind has lost its once great civilization, now living in the ruins of the aftermath. But even though their lives are threatened by Gardeners — mysterious unmanned mobile weapons (of different ranks) sent from the Moon — brave teenagers have to become Gardener hunters to earn their living. And although human civilization at large lies in ruins due to high-tech maintenance free technology, some parts of the remaining cities still work in limited ways, supporting the humans living there. One fateful day Tokito Aizawa meets Tea, awakening a power older and beyond that of the Gardeners, and inadvertently opening up the door to a possibly much brighter future for the remainder of mankind...