There's a little bit written about it on Wikipedia but I wish I could find the documentary: https://en.wikipedia.org/wiki/Lemmings_(video_game)#Developm...
Also, if you're not being facetious and actually didn't notice, they do have a youtube embed of the full documentary made in 2022 at the bottom of the linked article. I haven't taken the time to watch it, but maybe that's the one you're thinking of
"Dad, are they playing Lemmings music?"
"It's called Pachebel's Canon, it's from the 17th century!"
https://m.youtube.com/watch?v=QwXthGJfHLc&t=118s
(And I choose that one as the forlorn, mournful sound seems most appropriate as all the lemmings march to their death.)
Documentary: https://m.youtube.com/watch?v=RbAVNKdk9gA