Although it's never explicitly stated, we know The Lion King is set somewhere in Africa. How? Prepare for some serious headcanon:
The setting, with its tall grass and quadrupedal wildlife, resembles the African savanna pretty closely. The opening song and the phrase "Hakuna Matata" are in Swahili, which is a language spoken in a number of East African countries, including Kenya and Tanzania. And since the producers researched the film in Kenya, we can probably conclude that Pride Rock and all of its animals are somewhere in Kenya.
Excuse us while we push our nerd glasses up a little higher on our noses.
Unless you're a scholar of anthropomorphic animal history (more universities should offer a degree in that), it's difficult to place The Lion King at any one point in time. All this could be going down in 1100 B.C. or 2080 A.D.—we'll never know, and it doesn't seem relevant to the plot that we do know.
Richard Hudson, the stage designer for The Lion King musical, confirmed this fact in an interview: "One of the most remarkable things about The Lion King is that it is not set in any specific time … the design possibilities were endless, so long as the scenery evoked Africa, and so long as it helped to tell the story."
For The Lion King, the micro elements of the setting are a lot more important to the development of the story than the macro ones. The time period is irrelevant, but Pride Rock, the elephant graveyard, and Timon and Pumbaa's jungle are extremely relevant.
The micro universe of The Lion King (i.e., its setting within Kenya) is a super moralistic one. It's basically a testing ground for rooting out good from evil.
In the film, we know that Pride Rock is the seat of goodness because Mufasa rules from there and the colors associated with it—gold, amber, yellow—are all regal in nature. To make things even more literal, we know from Mufasa himself that everything the sun shines on is his kingdom, which is to say that everything the sun shines on is good. Even when we leave the immediate vicinity of Pride Rock, this seems to be true: Timon and Pumbaa are good guys, and they live in a sunny place.
And where doesn't the sun shine? The elephant graveyard, for one. In case you don't remember, it's the place where Scar hangs out with the hyenas and makes dastardly plans to kill his relatives. We can safely assume that this part of the world is bad. To recap: sun = good. No sun = bad. The setting of The Lion King = highly moralistic.