Not that this is any indication of install userbase, but there are 117 repositories on GitHub that match "language:LilyPond"
Additionally, there are 90 people subscribed to the LilyPond subreddit on
reddit.com:
To really get a true measure of userbase, the best thing would be to modify lilypond itself to send a simple web request to something akin to Google Analytics, and track those numbers. It could even be "one in a thousand times" or something similar. Of course, this isn't going to ever collect data for people working offline, etc.
Otherwise, it's going to be pretty hard to guess total userbase size from things like mailing lists & GitHub.
From doing some web searches, I think there's a fairly significant use of LilyPond as "Something a little nicer than ABC that we use to engrave our church/choir/band's music" Unfortunately, I think MuseScore probably has a much bigger userbase for that use case though...
Steve