Start with the producer of the latest album that contains a performance of the song and go from there. Otherwise, hire a copyright attorney to search the title for you.
There are 340 songs by that title.
I cannot locate a song titled 'Stand By You' from The Lion King soundtrack.
Price Roy sings the song stand by me
If a song is on iTunes, chances are that there is somebody who holds the copyright rights to the song. If a song is copyrighted by someone somewhere other than YouTube, then the copyright will still apply when the content becomes available and able to be viewed on YouTube.
The song itself is in the public domain, but certain arrangements, performances, and recordings will have their own protection.
Ben E. King's "Stand by Me" was released on May 8, 1961.
Grove Park Music (a division of EMI) and Universal Songs of Polygram International.
The copyright for the song Makin' Whoopee by Walter Donaldson & Gus Khan is held by Donaldson Publishing/sga Obo Gilbert Keyes Music Co.
Abba performing Take A Chance On Me. (C) 1977 Polar Music International AB
Several divisions of EMI; EMI Blackwood would be a good place to start.
The song itself is handled by Golden World, but various arrangements, performances, and recordings may have additional rightsholders.