The Lion King is a movie, that I know when I saw it as a little kid, I started to cry about. It was so very sad when Simba's father died from the antelope. As a little kid, to watch that movie, and the emotional trauma involved and felt by Simba, it definitely effects how children perceive death. In case you haven't seen it or don't remember:
However, the rest of the movie portrays Simba's life as he grows up and matures into an adult lion who then desires to become king. The message of Hakuna Matata (No worries) is a great message to reveal throughout the movie. It helps to say to not let life get you down, and that things will work themselves out in the end.
Another message that is seen mostly in the beginning of the movie, is through the song, Circle of Life:
At a young age, Disney is teaching kids that we are all connected. That the Earth is not just ours, but the whole ecosystems. We are not alone, and all of our actions will have an equal and opposite reaction (Go Newton's 3rd Law!). The deep meaning and lessons shown throughout Disney movies, are not fully realized until you are older and then by then you have already learnt the lesson partially because of the movies.