I just watched the entire movie again a few days ago, and right away, this question popped into my mind afterwards. And to be honest, there is no one reason why I love it. Or even a few reasons. There are many, and most likely more than I can list or even recall, but there are several the really stand out.
1. The music. This is what has kept me liking the Lion King even when I wasn't very into it. I remember nearly crying after listening to CYFTLT after not hearing it for years.
2. The scale. Despite its short 90 minute length, TLK feels huge. Take the beginning: we have a cub who wants to be king. Many movies will have that be the movie and that's it. The second half: A broken young adult trying to find his place in life. Again, many movies will concentrate on just this, but The Lion King managed to include these two stories into one package, creating a very big movie.
3. The characters. Even simple characters such as Timon and Pumbaa have depth that makes you think twice abut them. Even Ed: is he really insane or not?
4. The fan-base. MLK right here is the surest of proofs. There are other great TLK sites, which is even better, but I have yet to find another such great community of fans.