I have freshly installed Mac OS 10.13.6 HIgh Sierra. Using lilypond 2.19.80, when specifying "Alegreya Medium" as the font name, whether the font is installed system wide for for just me, the example compiles but the Alegreya reverts to the lilypond sans default. Definitely not working right. And I cleared the lilypond font cache before starting.
\version "2.19.80"
\markup "test"
\markup \override #'(font-name . "Alegreya Medium") "test"
Andrew