organizing pieces with variables - lyrics not aligned

[Darren Ng]

In the following sheet,
"Dave" and "Ed" are not on the same line.

How to properly group melodies and their matching lyrics into variables,
while keeping lyrics on the same line?

    \version "2.24.1"
    segmentA = {<<
      { c4 c4 c4 c8 r8 }
      \addlyrics { Alice Bob Cathy Dave }
    >>}
    segmantB = { <<
      { d4 d4 d4 d8 r8 }
      \addlyrics { Ed Fred Greg Howl }
    >>}
    \score {
      \relative c'' {
        \clef "treble" \numericTimeSignature \time 4/4
        \segmentA
        \segmantB
      }
      \layout { }
    }