One of the many new forms of bending that was discovered during Avatar: The Last Airbender was lightning generation, and while Zuko could successfully redirect lightning that was shot at him, he couldn't generate his own. Throughout both Avatar: The Last Airbender and The Legend of Korra, benders around the world have discovered and mastered all sorts of bending techniques and sub-skills. For example, Toph impressively learned to bend metal in the heat of the moment, after being kidnapped. But that was only the start.
In The Legend of Korra, metalbenders were able to police the citizens of Republic City and even create their own city in the middle of nowhere. Earthbenders were also able to begin lavabending; waterbenders could heal people's bodies and spirits; and airbenders could project their spirits, even in the physical realm as Jinora impressively demonstrated from time to time. Getting to the point where these advanced bending techniques became commonplace, however, took some work - and quite a bit of time.
Azula displayed her ability to generate lightning in combat when fighting her brother, Zuko. And then later on, Zuko attempted to learn to make lightning himself. Unfortunately, he wasn't able to due to his repressed feelings and emotional turmoil - struggling between the light and dark; trying to appease his father, Fire Lord Ozai; and wanting to either capture or join the Avatar. It's unclear if Zuko ever learned to generate lightning since he never showcased the ability in Legend of Korra or in any of the comics. But given his power and growth, it's certainly possible he learned it.
Lightning generation became quite commonplace by the time of Legend of Korra's story. In fact, most advanced bending techniques were conventional during that time - and they were either used in daily life or by people in higher positions of the government or among the upper class of society. For instance, Mako was shown using lightning generation to power Republic City's electrical grid alongside several other firebenders in Legend of Korra season 1, and Mako had troubles of his own to work through. If lightning generation's usage was that widespread just decades after Avatar: The Last Airbender ended, then it's possible other advanced skills became more established as well.
But by the end of the original Avatar series, the only people who could generate lightning were Azula, Ozai, and Iroh - the latter of which did successfully teach Zuko how to redirect lightning, something that is notably difficult itself. So the fact of the matter is, Zuko could bend lightning, just not his own. However, that doesn't mean he wasn't worthy enough to do it; he accomplished a lot at a young age and was more than capable of taking on a task like learning lightning generation (if he had the time after becoming Fire Lord).