I would say that you're correct: it is true that Disney's The Lion King more closely parallels Hamlet than Macbeth. Consider, for instance, that both The Lion King and Hamlet involve a prince struggling to avenge the murder of his father and depose his treacherous uncle. Just as Claudius murders King Hamlet to gain power over Denmark, Scar murders Mufasa to take control of Pride Rock and the territory it controls. Following this act of treachery, Simba works to avenge his father's death and defeat his uncle, just as Hamlet tries to kill Claudius. It's true that The Lion King has some similarities with Macbeth (both involve characters who murder their way into power), but it's ultimately much more similar to Hamlet, especially since Simba parallels Hamlet rather than Macbeth.
That said, there are differences between The Lion King and Hamlet, especially in terms of the endings. The Lion King ends on a happy note with a victorious Simba taking control of Pride Rock, while Hamlet ends with the death of most of the play's main characters, including Hamlet himself. In this way, we can clearly see that Disney changed some details in order to make the story more kid-friendly. Since Hamlet is undeniably tragic and violent, this move is pretty understandable.