Apparently you can press the standing slash button to also throw (no idea how the game knows which of the two it wants to do...) but I haven't been able to pull this off in the entire game.

I got to the final fight at the very top of Pride Rock with Scar, weakened him to the point where he didn't attack me anymore, and spent 30 minutes trying everything to throw him and just had to quit.

EDIT: wow, too bad I didn't see this video: 7U0y7sXpM7w on Youtube

So the throw move is accomplished by pressing slash + jump simultaneously. Something the game never explains.

You can't post links yet, a few more rep and you'll be able to do it.
That way spambots can't attach links to words, like this. Or directly post links. If I remember correctly, you need at least 10 rep.

For anyone interested in watching, this is the youtube video:

https://youtu.be/7U0y7sXpM7w