Lightningbending used to be one of the rarest forms of bending in the Avatar universe. By the end of The Last Airbender, the only characters shown to be capable of it were Fire Lord Ozai, Princess Azula and General Iroh, all of whom are Fire Nation royalty. Zuko famously never managed to learn how to produce lightning himself, settling instead for redirecting others' attacks. But could he have passed his mental block by the series' end?
While trying to help his nephew understand lightning better, Uncle Iroh described it as a pure expression of firebending. However, lightning cannot be powered by rage or emotion. To perform lightningbending, one must have complete peace of mind. As Zuko found out, even letting the slightest bit of subconscious emotional turmoil influence one's bending makes it impossible to produce lightning at all.
Zuko's bending during Book 2 of The Last Airbender was also a lot more forceful. The very first firebending tip Iroh gave him was to power his attacks with his breath instead of his muscles, but it seemed this still hadn't fully sunk in. On his first attempt at lightningbending, Zuko rushed through his practice form, completing it with a final push that created an explosion in his face instead of producing lightning. It's clear he wasn't ready for lightning yet, both mentally and in terms of his bending skill.
Powering his bending with emotion worked alright for Zuko until Book 3. When he rejoined the Avatar and tried to teach him firebending, he discovered he'd lost almost all of his bending. Since Ty Lee or any other chi blocker hadn't touched him recently, Zuko and Aang concluded that his power was weakened because of his allegiance shift. Since Zuko's rage and desire to capture the Avatar had fueled his abilities from his introduction, joining Aang and his crew had removed the primary source of his bending, leaving him powerless.
Their solution was for Zuko to relearn firebending from a source as close to dragons -- the original firebenders -- as possible. He and Aang set out to visit the ruins of the Ancient Sun Warrior civilization in hopes of getting inspired by the teachings they'd left behind. They never expected to find actual Sun Warriors, however, so it was quite a shock when they discovered the centuries-old civilization still thriving.
When the Sun Warriors learned why the duo had visited, they tasked them with returning a piece of their Eternal Flame to their mysterious masters, Ran and Shao. Zuko and Aang's performance during this task would determine whether the masters would reveal the secrets of firebending to them, or destroy them. Despite some mishaps on their journey, the masters, who were revealed to be dragons, accepted both Zuko and Aang and taught them the original essence of firebending.
After this encounter, Zuko learned that firebending was about more than just power and destruction. He realized fire was pure energy, the basis of all life, and that fueling it with anger perverted the ancient art. Losing his firebending turned out to be a good thing in the long run as it enabled him to fully come to terms with his new goal in The Last Airbender: helping the Avatar defeat his father and restoring balance to the world.
Zuko never attempted to bend lightning after rediscovering how to firebend, but as he's moved past his original block, he should be able to right now. It's also possible he chose not to learn it for personal reasons. In his time, lightningbending was a purely offensive art. Since he could deal with it via redirection, he had nothing to fear from rival benders. Zuko aimed to become a Fire Lord who healed the world from his nation’s past regimes, so he had no reason to learn how to bend lightning -- but that doesn't mean he wasn't capable of doing so.
