As a singer/songwriter and musical-theatre performer I've always used and heard
lyrics except when referring to a specific word, phrase, or line, in which case we might say, "I'm forgetting the
lyric," "What's that
lyric?", "Let's change that
lyric," something akin to the way an actor might say "my lines" when referring to a large portion of a script, but "I dropped a line" or "I love that line" when referring to one spot or, well, one line. Of course, on the published sheet music it usually reads
Music by: and
Words by: (a distended period here?...I've never had to place a period after a colon before, how's that work?

)