Darth Vader can not use force lighting, because of his severed arms. Robotic hands can't summon the force lighting. However Darth Vader can still use other forms of the force, such as force choke.
Vader relies on the complex life support system of his suit to survive and it happens to be very vulnerable to electrical discharges. So, if Vader ever had unleashed Force lightning, there's a good chance it would've caused his suit to short circuit, thus, killing him.
Either way, while Vader can use most other Force abilities, Force Lightning needs to be channeled, and Vader's limbs are explicitly not connected to the Force. The Star Wars: Episode III - Revenge of the Sith Visual Dictionary confirms Darth Vader cannot use Force Lightning, and even suggests this is the reason why.
Weakness: Electricity
A lot of the systems that were keeping Darth Vader alive were maintained by electricity, which is why Force lightning was so destructive towards him.
It's likely Kylo never learned how to summon Force Lightning
He would teach and tell Kylo only what he wanted to, making sure that he stayed within limits and would certainly never get to the point of almost destroying him as Anakin did — therefore neglecting training in Force lightning.
Grandmaster Yoda himself was capable of summoning force lightning in the form of Emerald Lightning. Galen Marek was an extremely skilled user of this Force power, even after his conversion to the light side, rivaling Darth Sidious.
While Jedi could create Force lightning, like Sith, they choose not to use that power due to its association with the dark side and immoral nature. Despite being equally as strong in the Force, one innately Sith ability that Jedi in the Star Wars franchise do not wield is Force lightning.
Darth Vader's Insecurities are His Biggest Weaknesses
In the end, virtually all who have made the attempt to use Vader's cybernetic nature against him have ended up dead or defeated. The elite few who have had the upper hand, even before his conversion to mechanical monstrosity, have done so by dominating him mentally.
Given Rey's lineage as Palpatine's granddaughter, it is also reasonable to assume she is already better attuned to using Force Lightning than the average Force user, with Ben telling Rey that she has all of Palpatine's power within her at the beginning of The Rise of Skywalker.
1 Darth Sidious
As well as being a gifted bladesman Sidious' connection to the Dark Side is extremely powerful, granting Sidious the ability to conduct force lightning.
Over the decades, For lightning has become strongly associated with the Sith. Palpatine is particularly fond of this power, using it to most spectacular effect in Star Wars: The Rise of Skywalker.
The armor had ten protective layers, each made of very strong alloy that could protect Vader from some explosions and weapons. Vader had four artificial limbs as a result of his injuries on Mustafar and at the hand of Dooku on Geonosis. The apparatus of Vader's mask was designed to support his breathing.
Legends Canon: Yes he has. What he used was a variant of force lightning called “Emerald Lightning” which is supposed to be similar to Plo Koon's “Electric Judgement”.
Force lightning is a dark side ability used to torture, disfigure, and even kill one's victims. Blue in color, Sith shoot Force lightning from their hands by calling on their hatred and aggressive feelings. However, while a deadly weapon, it is not unstoppable.
Darth Krayt, Darth Wyyrlok, Karness Muur, Grand Master Yoda, Galen Marek and Revan were able to catch Force lightning with their bare hands. The latter three could also deflect Force Lightning back to its source.
Gray Jedi commonly demonstrated their skills with both Light and Dark side Force capabilities. For example, the capacity to construct a lightsaber from scratch, along with unique Force talents such as Force lightning.
1 Luke Skywalker
Having faced his father once before, Luke was familiar with his tactics and used the force to gain an upper-hand. In Star Wars Canon, only Luke Skywalker can be acknowledged as the one who truly defeated Darth Vader.
A Human male, Erv Lekauf was a lieutenant in the Imperial Army. In addition to his Imperial career, Lekauf was married and had a child. He was the aide of Darth Vader, and one of his few trusted subordinates.
While the former Jedi Knight's aversion to sand has been a running joke to Star Wars fans for years, Star Wars: Darth Vader #26 added a tragic new dimension to Vader's hatred of seemingly harmless mineral particles by tying it to the all-consuming fear of loss that led him down the path of the Dark Side.
It's the intensity of reflected lightning and the channelling of such raw dark side power that are the catalysts for Palpatine's transformation. Perhaps the face that boils up to the surface is shaped by his dark side corruption, but the lightning is definitely the cause.”
Without question, the most powerful Force ability present in Star Wars is the Thought Bomb. It is created through an ancient Sith ritual where the Sith combine their dark side powers. If done successfully, the Thought Bomb can destroy all Force-sensitive beings unfortunate enough to be within the radius of its blast.