Honestly the ONML music is somewhat lacking in variety compared to Lemming's. 5 out of 6 are in a major key (as opposed 12 out of 17 in Lemmings) and I'd labeled 1, 3, 5, 6 (in DOS ordering) as all "generically happy/upbeat" (2 I'd labeled "wacky/humorous" instead). I'm not at all surprised that CodieKitty didn't bother at all with the ONML music.
The only thing that kind of stands out for me is that I always found DOS's version of #3 to be kind of Christmas-y, because the instruments it uses sound kind of like bells and the melody is cheerful. (And perhaps it helps too that Tame 3 where that music is first featured, uses the Snow set.) But that's quite particular to the DOS version; versions like Amiga's use primarily brass instruments instead, and don't have quite that same feel to me.