They are quite simalar. But at least it has a happier ending.

I'd say that TLk 1 is more like the story of Horus: An egyptian story. There's Mufasa and Scar/Taka. And theres Osirus and Seth. Osirus becomes king, Seth gets jealous, same with the lion king. Simba's born, Horus is born. Seth kills Osirus, Scar kills Mufasa. Simba runs away, still the same in the egyptian story. Simba meets Timon and Pumbaa, Horus meets Thot. Simba reunites with Nala. Horus reunites with his mother. Simba, Timon, Pumbaa and Nala go back to Pride rock to stop Scar. Same with Horus. Horus stabs Seth. Scargets eaten. Horus becomes king. So does Simba. So similar.

Still, The lion king 2 is almost like Romeo and Juliet. But don't listen to me blab on any more.

It does seem similar, because they are inspired from these two stories. So yes stories have plenty of similarities. But not every detail is copied.

Also did you know that TLK3, also known as TLK 1 1/2, was inspired from another source? Here is quote from IMDB:
While the original Lion King movie was based on "Hamlet," this film clearly takes its inspiration from the play "Rosencrantz and Guildenstern are Dead" which features the events of "Hamlet" through the eyes of two minor characters.
Source: http://www.imdb.com/title/tt0318403/trivia