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.
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.
It's likely Kylo never learned how to summon Force Lightning
From what we learned from the Marvel Comics story on Kylo Ren and his upbringing, along with the information explained and even alluded to in the sequel trilogy — it's entirely likely that Kylo never completely learned how to harness Force lightning.
Force lightning ability was not restricted to dark-siders. Jedi and other light-siders who were strong of will and character could learn this power without falling to the dark side—but its use was viewed as inherently corrupting, and most Jedi Councils forbade its use.
Maul was a Force-sensitive Dathomirian Zabrak male who established himself as a crime lord during the reign of the Galactic Empire. He was once known as Darth Maul when he was the apprentice of Darth Sidious, and therefore, a Dark Lord of the Sith.
Anakin Skywalker, the Chosen One born of a mother but no father, had more midi-chlorians than any Force-sensitive of his era, surpassing all Jedi and even Yoda at over twenty-thousand.
Later stripped of his black Nightbrother markings, Maul was left solely red-skinned. Agonizing Sith tattoos were applied personally by Darth Sidious in an attempt to cleanse Maul's mind as well as demonstrating Maul's complete dedication to the dark side.
Jedi DID Wield A Form Of Force Lightning In Legends
It was considered forbidden by the old Jedi Order, although a few masters - such as Plo Koon - studied the technique and even used it on occasion.
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.
1 Darth Sidious
There has been no Sith, as powerful, meticulous, nor as evil as the Emperor himself, Darth Sidious. As previously mentioned, Sidious trained in the Dark Side by Darth Plagueis before Sidious killed Plagueis in his sleep, making Sidious a Sith Master.
He may have assumed he would have more time to train Luke before then, or that Luke would be skilled enough to manage. Second it might be that Yoda was so at peace or so one with the force by his death that he either could foresee the outcome of the fight or was willing to accept things as they happened.
Snoke using a short burst of Force lightning to subdue Kylo Ren. Other dark side wielders besides the Sith were able to harness the ability. Mother Talzin conjured her own version of Force lightning that was powerful enough to block Sidious' lightning. The Son used red lightning to attack his sister.
He tried, but was unprepared for the sheer power of Sidious' blast. It was magnitudes of order more powerful than Dooku's lightning, and it overwhelmed the defenses Yoda tried to throw up against it. Yoda just had no idea it would be so much stronger than what Dooku was able to muster.
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”.
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.
Anakin is supposedly more powerful than other Sith Lords like Dooku yet he can't use force lighting.
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.
Some Jedi are explicitly shown using red lightsabers in Legends, however. This includes Adi Gallia, Even Piell, Depa Billaba, A'Sharad Hett, and even Luke Skywalker.
In The Rise of Skywalker, it was revealed that Rey was actually the granddaughter of Emperor Palpatine. It's possible that Rey's ability to use Force lightning was an inherited trait, passed down from her grandfather. This would explain why Rey, a Jedi, was able to use a power typically associated with the dark side.
Force lightning is a dark side ability used to torture, disfigure, and even kill one's victims.
The end of George Lucas' prequel trilogy instead proves that Palpatine's face changes as part of his plan to manipulate Anakin, with Palpatine using the Force to hide his true visage up until that moment.
Electric Judgment, also known as Emerald Lightning, was a Force power used by the Jedi to spray electric bolts of variable intensity from the hands and fingers.
Regardless, Dooku's eyes weren't yellow because he wasn't motivated by anger. He was merely a practical dark side user, so he does not have the usual Sith eye color.
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.
Darth Maul died during a final battle with Obi-Wan in the Rebels TV series, and Palpatine couldn't have cared less. For him, finding and killing Maul for his failure simply wasn't worth the effort.