Here're the Acorn Lemmings and ONML music in their original MOD format. Because there are multiple songs in a single MOD, you'd need to find a specialized MOD player with the ability to start playing at particular song positions, such as
ModPlug Tracker, in order to hear all the songs in a MOD past the first one. I'll look into the task of separating out the songs into individual MODs sometime later. (You can also try doing that yourself with ModPlug Tracker, which also supports other handy features like conversion to MP3 I think.)
For those who don't want to bother but still curious about the Acorn ONML music, here's a quick sample of tunes I recognized from its set of 26 tunes: Three Blind Mice, William Tell, Greensleeves,
Mary Had a Little LambO MacDonald Had a Farm, Trepak (Russian dance) from The Nutcracker, Bach's Toccata and Fugue in D minor (pretty recognizable organ music), and that slower 2nd half of the Circus theme in Lemmings 2.