Lemmings and its expansion packs used a custom format called "SoundPlayer", written by Scott Johnson of DMA Design. I believe the name comes from a string seen inside the replayer code.
* The music as found on Amiga Lemmings disks: https://www.exotica.org.uk/wiki/SoundPlayer
* Source of replayer code: http://wt.exotica.org.uk/players.html
Lemmings 2 and the All New World of Lemmings used MED by Teijo Kinnunen, as did most later DMA Design titles (Walker, Hired Guns)
The port of Lemmings to the Acorn Archimedes actually used a MOD file, presumably because Protracker is not native to the Acorn, but it was a popular format at the time and several people had written replayers for the Acorn
While you say "the music was easily converted"... that's not always true. The SoundPlayer format, based on reading its replayer code, supports 38 sound samples. Protracker supports 31 samples at most. Had the Lemmings music _used_ 38 samples, converting to Protracker would've come undone.
Similarly, while MED can be converted to Protracker, Protracker doesn't support all MED's commands, timings, synthetic instruments, and it actually does sound different and worse... provided the music made any use of those extra capabilities.
Quite a few games did have CPU-intensive mixing for multiple sound channels, but only as title-screen music, not in-game. Famously there is TFMX 7V format used by Chris Huelsbeck (Turrican 2, Turrican 3, Apidya, Metal Law) but also Hippel 7V used by Jochen Hippel (Amberstar, Ghost Battle, Lethal Xcess) and Oktalyzer. Furthermore, Super Stardust used the increased CPU capabilities of the A1200/A4000 to have its title music in ScreamTracker 3 (S3M) format.