Force Lightning might be a powerful technique used by the Sith, however, Darth Vader is never seen using Force Lightning in any of Lucasfilm's Star Wars movies.
However, this doesn't mean that Darth Vader doesn't have the ability to do so. In Star Wars: Darth Vader #5 by Charles Soule and Giuseppe (via Comic Book Resources) reveals how the legendary Star Wars villain used Force Lightning to create the kyber crystal for his own red lightsaber.
Unlike Jedi lightsaber which are created by making use of the power of a kyber crystal, it takes extra effort to create a Sith lightsaber. The Darth Vader series reveals the terrifying process of creating a Sith Lightsaber – a Sith lord must kill a Jedi master and bleed the kyber crystal of the weapon in order to give the lightsaber its red coloring.
In the fifth issue of the comic book series, we get to see Vader trying to "bleed" his saber, only to fail during the first try. He then sees a vision where he returns to confront Darth Sidious with a Jedi lightsaber, choosing the Light Side of the Force. Defeating Palpatine, Vader returns to Obi-Wan and kneels before his former master with his helmet off. This vision represents Vader's failed attempt at bleeding the kyber crystal of the weapon he took from Jedi master Kirak Infil'a.
Angered by his failure, Vader tries to bleed the cystal again, and this time he pours Force Lightning together with all of his pain and anger into the bleeding the kyber.
Vader nearly destroys himself and the planet of Mustafar in the process.
This is probably the main reason why Vader doesn't toy around with Force Lightning in the Star Wars movies. The Sith Lord may not want to try Force Lightning again after what he went through in Darth Vader #5.