Like most of the songs from Made In Heaven
(the exceptions being "Mother Love," "You Don't Fool Me" and "A Winter's Tale"), Freddie Mercury's vocals were taken from a previous recording. In this case it was from a 1983 unfinished demo for an unreleased song called "Another Piece Of My Heart," which was a collaboration between Queen and Rod Stewart.
The Rod Stewart vocals were axed for "Let Me Live," but the Mercury vocals weren't enough for a full song so Brian May and Roger Taylor stepped in and wrote new parts which they recorded. What that created was the only Queen song where all three of the group's vocalists sang lead. The choir-like harmony part in the middle of the song was done by session singers as Roger Taylor and Brian May probably couldn't recreate the three-part harmonies Queen was known for.
Kyle - Dallas, TX