Two easily explainable reasons for why Maul never used Force lightning, which have come up several times, are one) that he wasn't a Sith Lord and two) he never learned the ability in the first place.
Force lightning almost always required a living conduit for the energy to be channeled; thus Darth Vader, despite being an immensely powerful Sith Lord, was never able to properly employ this ability, as any attempt to generate it carried the risk of shorting out his life support systems.
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.
This could change over time as Cal succumbs further to the dark side's allure, so his Force Lightning could start off stunning his opponents before inflicting damage, then ultimately being used to kill.
Dooku first used Force lightning at a young age. According to the audiobook, Dooku: Jedi Lost, he was once abducted for a Dark Side ritual, conjuring lightning to kill his captors and escape. Dooku went on to become one of the greatest Jedi masters, but his ability to use lightning was seemingly a natural talent.
Why Darth Maul Never Used Force Lightning - Star Wars Explained
Could Kylo use Force lightning?
Kylo demonstrably couldn't defeat Snoke directly, instead killing his master via deception. Kylo most likely never learned how to conjure Force lightning, which is considered an advanced skill for dark side users.
Cal Kestis is more powerful than Luke given how easily he exercises his Force abilities. Not only does Cal possess the rare Force ability psychometry, which allows him to see an object's past by touching it, but he also lifts and pushes things without expending much effort.
Within the franchise, Cal is a former Jedi Padawan and survivor of the Great Jedi Purge who, during the early reign of the Galactic Empire, lives in seclusion on the planet Bracca until an incident forces him to reveal his Force powers.
Furthermore, Cal's mastery of multiple lightsaber stances is far superior to Luke's mastery of one. This allows Cal to use a combination of fighting techniques to deal with difficult situations, especially where there are lots of enemies. In these situations, Luke could easily be overwhelmed and fall.
Anakin Skywalker's Chosen One Potential Was Permanently Stunted. The Darth Vader comic book series reveals that, while the eponymous Sith Lord was indeed capable of using Force Lightning, the electricity could potentially destroy his life-sustaining suit.
Due to Vader's mechanical suit, he cannot interact with lightning under the pain of suffering malfunctions in the vital life support systems he uses. This is a rare problem for him to come up against, due to only other Sith commonly utilizing such a capability.
She and Kylo Ren were both trying to bring the transport to themselves with the Force, and in her anger, she accidentally unleashed lightning upon it, destroying the ship immediately.
Mace Windu, with his lightsaber combat form Vaapad, could reflect the lightning back to its source with a "superconducting loop". It required tremendous effort on the reflector's part, however, as seen in Windu's battle with Palpatine; Windu was seemingly able to overcome Palpatine's lightning.
Cal Kestis and Starkiller come from vastly different places, but they may be two sides of the same coin. One was forged by Vader while the other one was forged by rebellion, but they both ultimately do what is right in the end.
The fact that Kestis, who was shorter in his training than Ahsoka, was eventually able to defeat her is a good indicator that she wouldn't survive her fight with Ahsoka who even without her lightsabers was already able to defeat other Inquisitors.
By the end of their duel, Cere left Vader burnt, limping, and wheezing, proving Vader wasn't all-powerful. Ultimately, she came closer to killing Vader than almost any Jedi in Star Wars canon, though her overzealous attack ended up being her downfall.
Jet: Well, that's simply because this was an in-universe match, the characters are both jedis and have the same level of strength and speed in feats for the most part, the battle really just came down to whose more skilled, and quite simply Cal has defeated enemies Ezra couldn't, fought enemies Ezra has never had, and ...
For one, Cal can't kill Darth Vader because of what's already been established in the lore and continuity that was created long before Cal ever appeared in the Star Wars Jedi franchise.
Like his master, Darth Sidious, better known as Sheev Palpatine, Maul's main weakness was his overconfidence. In Luke Skywalker's confrontation with Palpatine during The Return of the Jedi, he tells the Emperor that his overconfidence is his weakness.
Regardless, based on the season 7 of The Clone Wars, and the fact that Darth Maul was aware of Anakin Skywalker's future and his role as the Chosen One, it is very likely that Darth Maul indeed feared Darth Vader to some extent, and preferred to avoid a direct confrontation with him, at least, on his own.
