At this point, it might be fair to say that Star Wars: The Last Jedi is one of the most divisive movies to come out of pop culture in recent memory. Even now, more than three years after its release, fans of the franchise are still arguing over it. Some loved the new approach that it took to Star Wars and the way it portrayed the characters, while others hated it for those exact same reasons. One of the most heated topics is the way in which the film handled Luke Skywalker and his change in personality.
In The Last Jedi, Luke is living on an island as a hermit and is much more jaded and sarcastic, very different from the upstanding hero we saw at the end of Episode VI. Some fans felt that this betrayed George Lucas's original design for the character and didn't carry on the legacy of the franchise properly. As it turns out, this version of Luke was actually something that George Lucas had planned all along.
It is revealed in the book The Art of Star Wars: The Last Jedi (via Den of Geek) that a lot of the story beats regarding Luke's character actually came from concepts that George Lucas had originally planned for a potential Episode VII. Originally, Lucas had the idea for an older and more jaded Luke teaching a young Jedi hopeful named Kira (who later became Rey). Apparently, Lucas even sat in on the initial creative meetings at Disney for Episode VII in 2013, and the original ideas for the Jedi temple and the designs of Luke and Kira were decided in these meetings.
Disney's acquisition of Star Wars also meant that they had the rights to Lucas's ideas for the Sequel Trilogy, and Lucas had planned to be a behind-the-scenes consultant on The Force Awakens, imparting his ideas to the filmmakers to help them craft Episode VII. J.J. Abrams, director of The Force Awakens, eventually scrapped a lot of the ideas that Lucas had for Episode VII and went in a different direction. The irony in this is that certain fans criticize Rian Johnson for straying too far from the "original vision" of Star Wars and praise Abrams for staying truer to that original intent, when it appears it was actually the other way around.
Rian Johnson took inspiration from those ideas that Lucas had for Episode VII and transferred some of them into The Last Jedi. In Lucas's vision, Luke is living sequestered on a far away planet after the events of Episode VI. A Force-sensitive girl named Kira finds him, and he begins to train her as a Jedi. Luke would eventually regain his confidence and fighting spirit while training Kira, and would join in the battle himself once again.
There was also a plan to have Luke struggle with his failure to stop the "Jedi Killer" (who eventually became Kylo Ren in the Sequel Trilogy) from destroying the Jedi Academy. Obviously, all of these story ideas made it into The Last Jedi in some form or another (though it seems they - perhaps unfortunately, depending on tastes - decided to scrap an idea that involved Luke being haunted by a Sith ghost for the duration of the movie).
In general, Disney made the decision to scrap a lot of George Lucas's original plans for the Sequel Trilogy, and most of his ideas were just that - ideas. He never wrote scripts for the Sequel movies, so there's no evidence of whether or not he had a clear plan in his mind for the exact places the story was supposed to go, or whether the Sequel movies that did get made lived up to his expectations. Clearly, there was one Sequel movie that utilized his initial plans for the story, and it would be interesting to learn why Disney and the teams that worked on Episodes VII and IX weren't as receptive to Lucas's ideas.
Mark Hamill himself even said that he wished that George Lucas had been more involved in the making of the Sequels, and that they would have consulted him for guidance and inspiration. Hamill claims that Lucas did have a general outline for the three Sequel movies, and that what Disney ended up putting out was very different from that original intent.
However, it's nice to see that some of Lucas's creative input did get used in the final cut of the movie, and that Rian Johnson decided to weave Lucas's original idea for Episode VII into The Last Jedi. Some fans may criticize it for its subversiveness in the Star Wars universe, and particularly for "changing the personality" of a beloved hero, but that was an idea that George Lucas wanted to explore all along. Getting to see a different side of the nearly infallible Luke Skywalker was an interesting move, and sets The Last Jedi apart from other films in the franchise. Even if his original outline was never used in full, at least some of George Lucas's ideas made it into the final installment of the Skywalker Saga, and the series was at least able to honor him in that way.