Hi Bob:
That "La Danza" (in
The Great Caruso)
was pre-recorded, although I know it does look as though it's being performed live. We have the MGM recording log for it, and the original acetate can be heard on the 2022 Sepia Records CD
The Undiscovered Mario Lanza. (Lanza sounds even more vibrant on the acetate, as there's no compression.)
In any event, if you watch the pianist's hands immediately before Lanza starts singing, you'll see that they're out of sync with the actual recording :)
Cheers,
Derek