Writing The Lion King.

Animated Views has an interview with the directors of The Lion King, Roger Allers and Rob Minkoff, on the occasion of the film's 3D rerelease and has this titbit on the subject of its Hamlet similarities:

"RI: Many people have noticed similarities to Hamlet in the story of The Lion King. Was that something you were conscious of when making the movie?

RM: Because The Lion King was considered an original story there was always the need to anchor it with something familiar. When we first pitched the revised outline of the movie to Michael Eisner, Jeffrey Katzenberg, Peter Schneider and Tom Schumacher, someone in the room announced that Hamlet was similar in its themes and relationships. Everyone responded favorably to the idea that we were doing something Shakespearean and so we continued to look for ways to model our film on that all time classic. Shakespeare is the greatest dramatist in history. His works have stood the test of time like no other. But it takes time to learn to appreciate Shakespeare and I was fortunate enough to grow up in Palo Alto California, in a time and place where arts education was supported."

So the film wasn't originally pitched as a Hamlet remix but those elements were brought in later [previously].