Musicals are sometimes edited a little to make them a bit more fresh and exciting. Before Cats closed in London *grumbles* they did this quite often.
To the best of my knowledge Rafiki starts singing He Lives In You and Simba joins in near the end in the background. I have the Broadway recording and that's what happens.
I don't think Simba ever sang one of these songs by himself.
Anyway, hiya! *waves a paw*