\header { tagline = ##f }

\layout {
  \context {
    \Lyrics
    \override VerticalAxisGroup
              .nonstaff-nonstaff-spacing
              .minimum-distance = ##f
  }
}

aliceSings = \markup { \smallCaps "Alice" }
eveSings = \markup { \smallCaps "Eve" }

<<
  \new Staff <<
    \new Voice = "alice" {
      f'4^\aliceSings g' r2 |
      s1 |
      f'4^\aliceSings g' r2 |
      s1 | \break
      % ...

      \voiceOne
      s2 a'8^\aliceSings a' b'4 |
      \oneVoice
      g'1
    }
    \new Voice = "eve" { 
      s1 |
      a'2^\eveSings g' |
      s1 |
      a'2^\eveSings g'
      % ...

      \voiceTwo
      f'4^\eveSings a'8 g' f'4 e' |
      \oneVoice
      s1
    }
  >>
  \new Lyrics \lyricsto "alice" {
    may -- be
    sec -- ond
    % ...
    Shut up, you fool!
  }
  \new Lyrics \lyricsto "eve" {
    that the
    words are
    % ...
    …and then I was like–
  }
>>