It is common, but it is done via \override and not \markup.
%%%%
fancyText = {
\override LyricText.font-shape = #'italic
\override LyricText.color = #red
}
\new Lyrics \with { \fancyText } \lyricmode { a b c }
\new Lyrics \lyricmode { \fancyText a b c }
\new Lyrics \lyricmode { a \once \fancyText b c }
%%%%
If you need to apply arbitrary \markup commands to all lyrics, you
could install a transforming procedure that operates on each
individual LyricText:
%%%%
transformText =
#(define-music-function (transformer) (procedure?)
#{ \override LyricText.text = #(grob-transformer 'text
(lambda (grob orig) (transformer orig))) #})
boxify = #(lambda (text) #{ \markup \box #text #})
jitter = #(lambda (text) #{ \markup \rotate #(- (random 20) 10) #text #})
\new Lyrics \lyricmode {
\transformText \boxify lorem ipsum dolor sit amet
\transformText \jitter lorem ipsum dolor sit amet
}
%%%%
-- Aaron Hill