Hi Martin and All,
What you say is true, but is is also the case that distributions, rather than being just branding or naming on top of Linux, tend to focus on certain aspects and become established for that. Debian example lags behind the leading edge to focus on stability. Ubuntu tries to focus on ease of use. Centos focuses on rock solid heavily tested stability and features that ISP's and technical installations require (such as our world class Synchrotron facility here in Melbourne, and various astronomical observatories). Arch focuses on a fine grained do-it-yourself build model that gives advanced users a very bespoke solution. Some don't come bundled with a desktop because they are designed for server applications primarily. Some focus on compactness for devices.
So I think it is worth the OP knowing about this when faced with so much choice.
In relation again to the original question regarding which distros lilypond runs well on, it does seem to run nicely on all, except that as stated before, I have run into strange difficulties with lilypond only on OpenSUSE Leap 42.1. But I discarded this distro more to ongoing incompatibilities with Virtualbox than lilypond problems.
And finally, the question is of course similar to 'which camera is best?', which topic flows on through photography forums continuously, with no resolution, obviously. And yet, people like having these discussions. There is an anthropological tribal aspect to this, of people wanting to belong to an identifiable group.
Andrew