I'm Lum the Notorious! - It's Raining Oil in Our Town
1-1. I'm Lum the Notorious! This episode opens with a baseball game and Ataru getting hit with a left field flyball. Ataru is soon escorted home and discovers he's been chosen to fight an invading alien force's champion in a 10-day game of tag. If he loses, the aliens will invade. But if he wins, the aliens will go home. Ataru isn't at all willing to play tag until he sees the alien's champion: the beautiful Lum. 1-2. It's Raining Oil All Over Town This episode opens with Ataru friends Megane and Lum's Stormtroopers at school who are watching films of the tag game. In this episode, a space taxi gives Ataru a ride home by accident and the fee is...too much. Since Ataru cannot pay, the space Taxi Collection Agency starts stealing all the oil in the world.
Aired 14/10/1981EP 1 - I'm Lum the Notorious! - It's Raining Oil in Our Town

Urusei Yatsura
It all begins when aliens invade and threaten to conquer the Earth! However, one member of the human race is chosen at random to duel the aliens and save the planet: Ataru Moroboshi, a lecherous slacker from Tomobiki High School who begrudgingly participates. All he has to do? Play a game of tag and catch Lum — the beautiful alien princess in a tiger-stripe bikini — by the horns. Unfortunately for Ataru, it’s not so simple, since Lum can fly and deliver electric shocks! Perseverance pays off, but once he catches her, Ataru experiences another shock: He’s now Lum’s betrothed “darling” and she isn’t going back to her home planet anytime soon!
(Source: Crunchyroll)