We all know that lightning is electricity, and electricity runs easily through metal. And since the shafts of umbrellas are usually metal, it follows logically that lightning likes to strike umbrellas!
Generally Played for Laughs, it's rare that any lasting injury happens to a character who has this happen to them; apart from the usual effects of such slapstick humor, usually the worst that happens to the character is that their umbrella gets ruined, and they get cold and wet, when in reality, lightning kills or seriously injures people.
There's a certain amount of irony in this trope: you carry an umbrella to protect yourself from the fury of a storm, and when this happens, it's as if the storm is invoking Improvised Lightning Rod on your umbrella to punish you for the audacity to think you have the right to stay dry!
As far as Truth in Television goes, storms are miles wide and miles high, and when you take that sense of scale into account, having a meter-long-at-most piece of metal in your hands isn't going to have an appreciable effect on the storm's target selection. That being said, the way you keep yourself safe from lightning is to not be outdoors during a lightning storm in the first place.
Note: If an umbrella literally has a lightning rod built in, that either implies this trope by saying lightning hits umbrellas often enough for a lightning-rod feature to be needed, or else it invokes the trope if one or more characters actually want lightning to hit the umbrella. If lightning actually hits the umbrella, then it's this trope played straight.
- A Clorox Rain Clean Bleach commercial showed two anthropomorphic bottles of bleach wearing rain gear to try to masquerade as having scent-after-rain freshness, themselves. One of them uses an unlucky open umbrella indoors as part of his disguise, despite being warned it's bad luck. Cue him getting zapped by lightning and given an I Told You So in The Stinger. https://www.youtube.com/watch?v=iGqyzwg6GRU
- Katekyō Hitman Reborn!: Inverted and weaponized with a character named Levi who always carries 8 umbrellas that can shoot lightning.
- Kirby of the Stars: Again, inverted and weaponized with Kirby's Parasol power in the anime: his umbrella can fire lightning at his enemies. However, it's worth noting that the Parasol powerup doesn't have this effect in the Kirby games.
- The Blue Umbrella: a novel by Mike Mason tells of a boy whose mother died due to a lightning strike that, evidence shows, hit her umbrella while she was walking in a field. This is not played for laughs at all, and there's comments in the novel that his mother knew better than to be in a field with an umbrella during a lightning storm, but she didn't think it was a lightning storm at the time.
- Tank McNamara: In one comic about lightning delays for golf, Dr. Tszap invents an umbrella-hat that doubles as a lightning rod, and in the punch line, a storm is rolling in, heavily implying the golfer wearing the prototype is soon to get struck.
- League of Legends: Forecast Janna's /joke animation is a storm cloud gathering above her, then her opening her umbrella in reaction to said cloud, then said cloud zapping her umbrella.
- The Sims 3: The cover of the seasons expansion to this game shows a poor Sim in a thunderstorm, getting electrocuted through her umbrella by lightning.
- Deponia: Invoked in the Chaos on Deponia sequel where Rufus must trick Goal into holding an umbrella, among other lightning-unsafe activities such as standing in a wading pool, so that she'll be struck by lightning and he can climb a communications tower without being struck himself.
- Secret Agent Clank: Inverted and weaponized with the Thunderstorm Umbrella, a Shock and Awe weapon in the shape of an umbrella that fires lightning bolts at enemies.
- Bon Voyage, Charlie Brown: Snoopy carries an umbrella in a thunderstorm. He gets hit by lightning twice, once on his nose when he sticks his nose out the window, and then the second time hitting his umbrella and vaproizing the waterproof webbing.
- Mr. Bogus: In the Hipster Tripster episode, Bogus is given an umbrella to keep him dry in the rain, but lightning destroys it.
- In the Ad Bumpers of a Fox Kids cartoon, there was a caveman and a monkey who was generally more sophisticated than the caveman. In the pre-commercial bumper, the caveman's solution to being caught in the rain is to tear off two large leaves and hold them over his head. The Monkey's solution is to pull out an umbrella. In the post-commercial bumpers, the caveman convinces the monkey to trade, after which the umbrella gets hit by lightning.
- Johnny Bravo: In the episode Johnny meets Donny Osmond, Donny ends the episode by trying to float away with an umbrella, Mary Poppins style. But the umbrella gets hit by lightning and he crashes to the ground.
- In the Looney Tunes short "Porky's Badtime Story" (and its color remake "Tick Tock Tuckered"), Gabby Goat (Daffy Duck in the remake) is disturbed by a leak in the roof, so he opens an umbrella. Porky Pig warns him that it's bad luck to open an umbrella indoors, which Gabby/Daffy scoffs at. Then a lightning bolt enters the house and strikes the umbrella.